Geometry
Triangles, circles, coordinate geometry, and proof-oriented questions.
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van departs due north at 20 mph, starting at the same point and in the …
C. 50 miles
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multiple-choice question translate the triangle using the (x + 6, y - 1…
The correct option is the third one: E'(-2, -2), F'(6, 1), G'(9, -1) (i.e., the option with G(9, -1)).
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multiple-choice question subtracting 1 to the y coordinate of the point…
down (assuming there was a missing option 'down' as per the partial view, and based on the rule of coordinate transformation: decreasing y - coordinate moves the point down)
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why might francis scott key have written the star - spangled banner? op…
He must have felt joy and pride that the United States had been victorious at the battle of Fort McHenry.
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construct the following transformation on qt: y=3 q(0,7) t(4,3) q( , ) …
The coordinates of \( T' \) are \( (4,3) \) (the same as \( T \) because the distance from \( T \) to \( y = 3 \) is \( 0 \), so reflecting it over \( y = 3 \) leaves it unchanged…
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transformations test (topic 4) a translation is used to map ( a(-5, 13)…
\( B'(11, -6) \)
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multiple-choice question remember, adding 6 to the x coordinate moves t…
right (the option corresponding to moving the point right when 6 is added to the x - coordinate)
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what is the volume of this prism? 4 mm 10 mm 3 mm cubic millimeters
120
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geometry translations explained! ... the image of δefg after the follow…
Subtract 1
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mallory cameron geometry translations explained! what is the image of δ…
Add 6
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∠p and ∠r are complementary and ∠p and ∠q are complementary. complete t…
For Statement 4, the reason is "Definition of complementary angles".
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3. which of the following are impossible? give a reason for your answer…
d. A pentagon created by 5 rays is impossible. Reason: A pentagon is a closed polygon with 5 finite line - segment sides. Rays have one endpoint and extend infinitely, so 5 rays c…
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reflections over the x-axis and y-axis explained! click to watch the im…
To solve the problem of finding the new coordinates of point \( P \) after a reflection over the \( y \)-axis, we follow these steps: ### Step 1: Recall the Reflection Rule over t…
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3 which of the following are impossible? give a reason for your answer.…
12
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multiple-choice question a positive change in the y value shifts the po…
A. Up
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transformations test (topic 4) if the point ((x, y)) was translated 7 u…
\((x - 7, -y + 5)\) (the first option)
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multiple-choice question a negative change in the y value moves the ima…
Down.
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write the expression as the sine or cosine of an angle. cos 7y cos 3y −…
$\cos(10y)$ (So the first box is $\cos$ and the second box is $10$)
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1. new characteristics of the frog unfold; 2. the push of the crowd; 3.…
This appears to be a vocabulary matching exercise where we find the word with a similar meaning to the boldfaced word in each phrase. Let's solve a few (e.g., question 3, 4, 10): …
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multiple-choice question what is p? reflection rule x-axis p(x,y) → p( …
\((x, - y)\)
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given the following parallel lines and transversal, m∠2 = 7x - 20 and m…
x = 11
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transformations test (topic 4) given a regular pentagon (five - sided s…
224 degrees (the option with 224 degrees)
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multiple-choice question a change in the y value means the preimage sli…
Up or Down
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multiple-choice question a negative change in the x value slides the po…
Left (the option corresponding to "Left")
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given that ∠5 ≅ ∠6, which of the following would complete the proof tha…
2) Vertical Angle, 3) Vertical Angle, 4) $\angle 4 \cong \angle 7$ (the last option: 2) Vertical Angle, 3) Vertical Angle, 4) $\angle 4 \cong \angle 7$)
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complete the congruence statement. defc ≅ submit learn about congruence…
UVWX
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which statement proves ∠3 ≅ ∠5? diagram: two horizontal lines ( m ) (to…
A. Alternate Interior Angles Theorem
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two transformations are performed on δx in the coordinate plane. first,…
A. \(\triangle X\) is similar to \(\triangle X''\).
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given the following figure, solve for y. (7y + 27)° figure: two paralle…
\( y = 14 \) (corresponding to the option "y = 14")
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the x axis is the ______ line that passes through the origin.
horizontal
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what are the corresponding parts of the figures below? select all that …
The correct corresponding parts are: - \(\boldsymbol{\angle L \cong \angle S}\) - \(\boldsymbol{\angle K \cong \angle T}\) - \(\boldsymbol{\angle M \cong \angle R}\) - \(\boldsymb…
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open-ended question the x axis is the ____ line that passes through the…
\(y = k\) (specifically \(y = 0\) as it passes through the origin, and it is a horizontal line which has the equation form \(y=k\))
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choose the theorem that would best be used to prove the following state…
Consecutive Interior Angles Theorem
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multiple-choice question a change in the x value means the preimage sli…
right or left ### Second Question (About Vertical Line of Reflection through Origin):
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how does a translation change the preimage? flip rotate/turn slide
The checkbox next to "SLIDE" should be selected.
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who wrote the star spangled banner? john adams, francis scott key, elvi…
B. Francis Scott Key
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multiple-choice question how does a translation change the preimage? (a…
A translation changes the position of the preimage (moves it) but does not change its shape, size, or orientation.
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transformations test (topic 4) let x and y be the following sets: x = d…
\(\{45, 90, 135, 180, 225, 270, 315, 360\}\) (the third option in the given choices)
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proof of the same side exterior angle theorem. given: l || m prove: ∠1 …
B. 2. Corresponding Angles Theorem; 6. Substitution
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transformations test (topic 4) how many lines of symmetry does a regula…
B. 6 (assuming the option with 6 is labeled as B, matching the standard regular hexagon symmetry result)
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given ( l parallel m parallel n ), find the value of ( x ).
\( 61 \)
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given ( m parallel n ), find the value of ( x ) and ( y ).
\( x = 131 \), \( y = 49 \)
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transformations test (topic 4) 2 of 20 13:34 / 50:00 a nonagon is a nin…
60 degrees (and also 120 degrees? Wait, no, wait. Wait, let's re - check. Wait, the question is which angle would NOT map the figure onto itself. Wait, the rotational symmetry ang…
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10. (6y - 15)° (5x)° (4y + 25)° x = ________ reason: __________________…
\( x = 15 \) (Reason: Linear pair angles sum to \( 180^\circ \), and using \( y = 20 \) from alternate exterior angles equality) \( y = 20 \) (Reason: Alternate exterior angles ar…
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measure the length of each shaded bar using the provided rulers (each r…
# Explanation: ## Step1: First measurement (top) The object starts at 0 (implicit, since the left end is at the start of the ruler's visible part) and ends at 5.8 cm? Wait, no, lo…
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select all the pentagons.
All four figures (the top - left green - sided figure, the top - right blue - sided figure, the bottom - left blue - sided figure, and the bottom - right brown - sided figure) are…
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8. diagram with two horizontal lines and a vertical transversal, angles…
\( x = 65 \) Reason: The angle \((x + 25)^\circ\) and the right angle (\(90^\circ\)) are supplementary (they form a linear pair), so their sum is \(180^\circ\). Solving \(x + 25 +…
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multiple-choice question point q is the pre - image point. what are the…
A. (-2,-2)
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t(x-8, y+4) is our translation point p(3,0) is a pre-image point. what …
\(P'(-5,4)\)
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use the information to answer the question. a rectangular prism is show…
\( 26.93 \)
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4 figure ( r cong r ). describe a sequence of three transformations tha…
1. Rotate figure \( R \) 90° counterclockwise about the origin. 2. Translate the rotated figure up by 6 units. 3. Translate the vertically translated figure to the right by 9 unit…
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time a 6 foot person casts a 2 foot shadow, a nearby statue casts a ten…
30 feet (corresponding to the 30 feet option)
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a cylinder and a cone have the same base and altitude. if the volume of…
E. 90 cubic inches
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multiple-choice question where do we use rigid transformations? animati…
animation and video games
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reason: corresponding angles 4. (14x + 7)° 103 14x + 7 = 77 100° 77 x =…
\( x = 34 \) (Reason: Alternate Interior Angles are equal) \( y = 28.75 \) (Reason: Using the given equation \( 4y - 13 = 5x - 68 \) and substituting \( x = 34 \))
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multiple-choice question how does 4 affect the y value of the point? mo…
Move up 4
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multiple-choice question a movement of -8 on the 8 axis indicates we sh…
Left 8 (assuming the options are labeled as per the image, and the correct option is the one corresponding to moving left 8 units as a movement of - 8 on the x - axis indicates a …
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celeste is designing a water fountain for a city park. she wants one of…
C. 33.5 in
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10. refer to the segments. which segment is the image of fg when rotate…
segment AB
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multiple-choice question where do we use rigid transformations? animati…
A. animation and video games
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multiple-choice question which is the algebraic notation for this trans…
\((x - 8, y)\) (assuming the option with \((x - 8, y)\) is correct) ### Second Question (Rotation Requirements)
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multiple-choice question when a reflection happens, the shapes face in …
opposite
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multiple-choice question does a translation change the size of an objec…
No
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the blue figure slides to form the red figure so, the red figure is a t…
distance and the direction
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9. match the directed line segment to the image of polygon p being tran…
(Assuming the top \( P \) to \( Q \) uses directed segment \( a \), middle \( P \) to \( Q \) uses \( v \), etc.—but since the problem is to match, the correct matches are based o…
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(c) write a formula that relates the circumference, c, of a circle to i…
\( C = \pi d \)
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triangle qrs is shown with medians \\(\\overline{qv}\\), \\(\\overline{…
The ratio of \(WU\) to \(RW\) is \(1:2\) (if we correct the first box to 3, but based on centroid theorem, the ratio is \(1:2\)). Wait, maybe the given numbers are \(WU = 2\), the…
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triangle qrs is shown with medians \\(\\overline{qv}\\), \\(\\overline{…
\(1:3\) (or if we consider the centroid theorem correctly, it should be \(1:2\), but based on the given numbers \(2:6\), the simplified ratio is \(1:3\))
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the radius of a cylindrical water tank is 4 ft, and its height is 9 ft.…
\( 452\space\text{ft}^3 \)
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find a simplified expression to represent the area of the triangle. the…
The simplified expression for the area of the triangle is \( \boldsymbol{x^{2}+x - 2} \) \( cm^{2} \) (assuming a correction in the base and height values to match the expected fo…
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6 sarah draws figure efgh in the coordinate plane. she rotates figure e…
To draw \( EF'G'H' \), plot the rotated points: - \( E(1, -1) \) (unchanged, center of rotation), - \( F'(0, -3) \), - \( G'(-2, -3) \), - \( H'(-2, -1) \), then connect the point…
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a regular triangular pyramid has a base perimeter of 13.5 units, a base…
\( 8.8 + \frac{1}{2}(13.5)(6) \) (corresponding to the third option, assuming the options are labeled with the third one as \( 8.8+\frac{1}{2}(13.5)(6) \))
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5 △def ≅ △lmn. which sequence of transformations can be performed on △d…
A. Reflect \(\triangle DEF\) across the \(y\)-axis. Then translate the image 6 units up.
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4) the area of a trapezoid is found using: a = h(b1 + b2)/2 solve for h.
\( h = \frac{2A}{b_1 + b_2} \)
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part a two of these triangles are similar. select the two similar trian…
### Part A # Explanation: ## Step1: Calculate angles of each triangle For triangle \( EFG \): Angles are \( 68^\circ \), \( 74^\circ \), so the third angle is \( 180 - 68 - 74 = 3…
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kyle performs a transformation on a triangle. the resulting triangle is…
A. dilation
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the triangles below are congruent and their corresponding parts are mar…
(a) \( \angle A \cong \angle X \), \( \angle B \cong \angle Z \), \( \angle C \cong \angle Y \) (b) \( \overline{AB} \cong \overline{ZX} \), \( \overline{AC} \cong \overline{YX} \…
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the rectangle is made of unit squares. what is the area of the rectangl…
10
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select all shapes with a rectangle as a face.
The shapes with a rectangle as a face are the yellow triangular prism (second shape) and the pink rectangular prism (fourth shape).
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find the coordinates of the vertices after a dilation with a scale fact…
- A(-3, -5) connects to (-6, -10) - B(-1, 0) connects to (-2, 0) - C(-3, 5) connects to (-6, 10) - D(-4, 0) connects to (-8, 0)
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use the compass and ruler to construct the bisector of the angle below.
The angle bisector is constructed by following the steps of angle - bisector construction (placing compass at vertex, drawing arcs intersecting sides, then arcs from those interse…
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triangles abc and def are right triangles, as shown. triangle abc is si…
A. \(\boldsymbol{\frac{AB}{AC}}\), D. \(\boldsymbol{\frac{DE}{DF}}\)
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which graph represents the solutions to this inequality? 7m + 17 > -25 …
The top graph (with open circle at -6, closed at 5, and red line between)
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figure ( r cong r ). describe a sequence of three transformations that …
A possible sequence: 1. Reflect \( R \) over the \( y \)-axis. 2. Translate the result down 8 units. 3. Translate the new result right 2 units. (Adjust translations based on verte…
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the trapezoids are dilations using the center of dilation, point p. tel…
- A to C: Scale factor greater than 1 - B to A: Scale factor less than 1 - B to B: Scale factor is 1 - C to A: Scale factor less than 1
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shade in a rectangle with an area of 49 square units.
Shade a 7 - unit by 7 - unit square (or rectangle with length 7 and width 7) on the grid. (The actual shading would involve selecting a 7×7 block of the small squares in the grid.)
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mar decides to see what events the club has planned for the year. she g…
### Part B (Contesta) Answers: 1. To determine the club meetings: Looking at the "Reunión del club" icon, in October (OCTUBRE) it's on the 7th and 21st (both are jueves? Wait, no—…
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what is the area of this figure? figure with dimensions: 10 cm, 4 cm, 8…
179
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1 the vertices of a figure are given. what are the coordinates of the i…
Coordinates of image: \( M'(6,9) \), \( N'(15,9) \), \( P'(15,3) \); Type of dilation: Enlargement (since \( k = 3>1 \))
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what is the area of the shaded region? 17 mi 14 mi 10 mi 13 mi square m…
108
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4 figure ( r cong r ). describe a sequence of three transformations tha…
A possible sequence of transformations: 1. Reflect figure \( R \) over the \( y \)-axis. 2. Translate the reflected figure vertically (downward) by an appropriate number of units …
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find the circumference and the area of a circle with radius 3 m. use th…
Circumference: \( 18.84 \, \text{m} \) Area: \( 28.26 \, \text{m}^2 \)
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g is the midpoint of \\(\\overline{fh}\\). if \\(fg = 2x\\) and \\(gh =…
\( 4 \)
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the circle below has center v, and its radius is 5 ft. given that m∠wvx…
\(\frac{25}{6}\pi\) feet
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given ( m parallel n ), find the value of ( x ) and ( y ).
\( x = 41 \), \( y = 139 \)
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parallel lines and triangles 1. select all true statements if ( n paral…
### Problem 1 (Parallel Lines and Triangles, Select True Statements) #### Explanation: We use properties of parallel lines (alternate interior angles, triangle angle - sum) to ana…
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that you have learned to complete these problems. is a rotation of figu…
Yes, figure B appears to be a rigid transformation (translation) of figure A. Rigid transformations preserve parallelism, so the parallel sides of A remain parallel in B. For exam…
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△abc ~ △def. find the values of x and y. diagram: △abc (a bottom-left, …
a) \( x = 32 \) b) \( y = 1 \)
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which angles have the same measure as ∠e? choose all the correct answer…
A. \( \angle B \), C. \( \angle H \), E. \( \angle P \)
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practica la estrategia a cognados circle all cognates in the following …
To solve the problem of identifying cognates (words that are similar in Spanish and English due to shared etymology) and guessing their meanings, we analyze the underlined words: …