幾何
三角形、円、座標幾何、証明問題。
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question 1 1 pts what are the coordinates of the midpoint of the line s…
D. (-1, 0.5)
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a triangle has vertices a(1,2), b(3,4), and c(2,6). after a transformat…
b. \((x + 3,y + 3)\)
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a rectangle r has vertices p(0,0), q(4,0), r(4,2), and s(0,2). it is tr…
b. Yes, the figures are similar; a translation was performed.
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a triangle with side lengths 5, 12, and 13 is dilated to create a simil…
a. 6
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rectangle r with side lengths 4 and 6 is dilated by a scale factor of 2…
C. 8 and 12
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a triangle with vertices a(1,2), b(2,4), and c(3,6) is dilated to creat…
c. 2
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a rectangle has vertices a(1,2), b(5,2), c(5,4), and d(1,4). it is tran…
c. \((x,y)\to(x - 1,y - 2)\)
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if two figures are similar, which of the following must be true? a. the…
d. Their corresponding angles are equal
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if a rectangle is translated 3 units up and 4 units right, what happens…
A. They are increased by 3 in the y - direction and 4 in the x - direction.
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prices - additional practice formula: (total variable costs) / (1 - .pr…
1. The price of the shoes is $\$77.32$. 2. The price per burrito is approximately $\$3.67$. 3. The price of the car is approximately $\$17835.29$.
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2.3 homework question 6, 2.3.25 hw score: 23.81%, 5 of 21 points points…
The graph that shows the upper - half of the circle $x^{2}+y^{2}=49$ in red and the lower - half of the circle $x^{2}+y^{2}=49$ in blue is the correct one. Without seeing the actu…
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sketch the graph of the first function. then, on the same coordinate pl…
The graph where the red curve is the upper - half of the circle and the blue curve is the lower - half of the circle centered at the origin with radius 7. Without seeing the actua…
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sketch the graph of the first function. then, on the same coordinate pl…
The graph that shows the upper - half of the circle in red and the lower - half of the circle in blue is the correct one. Without seeing the actual options in detail, the correct …
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15. a rectangular park is 600 meters long and 400 meters wide. using a …
b. 30 meters
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14. two circles have diameters of 8 and 24, and their centers are 5 uni…
B. Dilation and translation
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13. if the scale factor of a dilation is ⅓, which of the following desc…
d. The image is a reduction of the preimage
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12. when the center of dilation is at the origin and the scale factor i…
d. The figure reduces to half its original size
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11. dilate point a(3, - 4) by a scale factor of k = 3 with the center o…
The coordinates of $A'$ are $(9, - 12)$ (Option b).
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10. the diameters of two circles are 12 and 36. what scale factor (k) i…
c. 3
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9. what does the center of dilation represent in a dilation? a. the lar…
d. The fixed point from which a figure is scaled
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8. an architect designs a skyscraper that is 100 meters wide. if the sc…
a. 5 meters
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7. a rectangular garden is 400 meters long and 300 meters wide. using a…
d. 40 meters
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6. a square with vertices at (1,1), (1,3), (3,3), and (3,1) is dilated …
d. $(2,2),(2,6),(6,6),(6,2)$
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5. a triangle △jkl with side lengths 4, 6, and 8 is dilated by k = 3. w…
b. 12, 18, 24
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4. a triangle has vertices x(1,1), y(5,1), z(3,4). after a dilation, it…
c. 3
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3. a city planner creates a scaled map of a residential area. the actua…
c. 10 meters
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are the triangles similar? explain why or why not. no, because point j …
Yes, because $\triangle{JKL}$ can be dilated by a scale factor of $\frac{1}{3}$ using the origin as the center of dilation and then the image can be rotated $90^{\circ}$ clockwise…
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7. graph the image of the triangle below using a scale factor of k = 4.…
For problems 7 - 10, we need the original coordinates of the vertices of the figures to find the coordinates of the dilated figures. For problems 11 - 12, we need the coordinates …
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4. rhombus wxyz with vertices w(2, -4), x(6, -2), y(10, -4), and z(6, -…
$W'(3,-6)$ $X'(9,-3)$ $Y'(15,-6)$ $Z'(9,-9)$ $D'(-1,3)$ $E'(2,2)$ $F'(2,1)$ $G'(-1,0)$
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3. rectangle pqrs with vertices p(5, 15), q(15, 15), r(15, 10), and s(5…
$P'(4,12)$ $Q'(12,12)$ $R'(12,8)$ $S'(4,8)$ $M'(-14,-8)$ $N'(-8,-6)$ $O'(-6,-12)$ $P'(-12,-14)$
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2. triangle lmn with vertices l(2, -8), m(12, 8), and n(14, -4): k = 1/…
$L'(1,-4)$ $M'(6,4)$ $N'(7,-2)$
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use the diagram to the left to answer questions 9 and 10. 9. if (mangle…
9. $122^{\circ}$ 10. $148^{\circ}$
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9. practice 2 use number sense explain why the numerical expression 3 l…
The expression "3 less than 16" is written as 16 - 3 because in the phrase "a less than b", we start with b and subtract a. ### 10.
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8. if m∠ecd is six less than five times m∠bce, and m∠bcd = 162°, find e…
$m\angle BCE = 28^{\circ}$ $m\angle ECD = 134^{\circ}$
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identify whether each pair is not similar, similar and has a scale fact…
Without specific coordinates of the vertices of $\triangle ABC$ and $\triangle DEF$ calculated, we cannot give a definite answer. But the general steps to determine are as above.
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6. if ∠def is a straight angle, m∠deg=(23x - 3)°, and m∠gef=(12x + 8)°.…
$x = 5$ $m\angle DEG=112^{\circ}$ $m\angle GEF=68^{\circ}$ $m\angle DEF = 180^{\circ}$
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question 11 (mandatory) (1 point) proportion & scale both relate to____…
D. Size
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5. if (mangle jkm = 43^{circ}), (mangle mkl=(8x - 20)^{circ}), and (man…
$x = 17$ $m\angle MKL=116^{\circ}$ $m\angle JKL=159^{\circ}$
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17.a solve the following problems. given: △abc, m∠a = 60°, m∠c = 45°, a…
\(P_{\triangle ABC}=\frac{27 + 9\sqrt{6}+9\sqrt{3}}{2}\), \(A_{\triangle ABC}=\frac{81(3+\sqrt{3})}{8}\)
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what is the least value for an integer, x, for which x, x + 5, and 2x -…
11
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in a certain triangle the length of two sides are 1.9 m and 0.7 m. what…
2
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it is possible that in a parallelogram with side lengths of 4 cm and 7 …
It is not possible.
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statements reasons 1. ∠1 and ∠3 are complementary a. 2. b. definition o…
$m\angle1 + m\angle3 = 90^{\circ}$
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in each case, use the new theorems to arrange the lettered measures fro…
$\beta$, $\alpha$, $\gamma$
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in the isosceles △abc, m∠acb = 120° and ad is an altitude to leg bc. wh…
$2\sqrt{3}$ cm
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in the isosceles △abc, m∠acb = 120° and (overline{ad}) is an altitude t…
$2\sqrt{3}$
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what is the area of an isosceles trapezoid if the lengths of its bases …
\(529\)
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what is the ratio of squares to hexagons?
2:1
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12.e solve the following problems. given: △mno, m∠m = 45°, m∠o = 30°, m…
$NO = 6\sqrt{2}$, $MO=3(\sqrt{3}+ 1)$
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12.c solve the following problems. given: △klm, lm = 12, m∠k = 60°, m∠m…
$18 + 2\sqrt{3}+4\sqrt{6}$
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in right $\triangle abc$ with $mangle c = 90^{circ}, mangle b = 75^{cir…
$18$
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7.b solve the following problems. given: △mop, p_{△mop}=12 + 4\\sqrt{3}…
$MP = 4$
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what is the ratio of hexagons to triangles? 7:□
7:1
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what is the ratio of circles to stars?
1
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what is the ratio of stars to circles?
2
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what is the ratio of triangles to rectangles?
$\frac{7}{1}$
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practice 3.1 scale factor and proportionality of similar figures 1) a m…
1. The actual height of the skyscraper is 300 meters. 2. The new side lengths of the triangle are $\frac{5}{2}$, 6, and $\frac{13}{2}$. 3. The scale factor from A to B is 2. 4. Th…
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7.b solve the following problems. given: △mop, p_{△mop}=12 + 4\\sqrt{3}…
$MP = 4$
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given a right triangle with legs a and b and hypotenuse c, find the len…
$4\sqrt{3}$
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what is the ratio of squares to hexagons?
1:2
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given a right triangle with legs a and b and hypotenuse c, find the len…
$4\sqrt{2}$
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2.b > what is the area of trapezoid abcd with bases $overline{ab}$ and …
$48\sqrt{3}$
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follow the guided instructions below to rotate the figure 180° counter …
# Explanation: ## Step1: Recall rotation rule For a 180 - degree counter - clockwise rotation about the origin, the rule for a point $(x,y)$ is $(x,y)\to(-x,-y)$. ## Step2: Rotate…
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convert the polar coordinates (5, 6.1) to rectangular coordinates. (0.9…
C. (4.92, -0.91)
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what is the area of trapezoid abcd with bases $overline{ab}$ and $overl…
\(48\sqrt{3}\)
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review the four points shown on the polar coordinate system. which poin…
point C
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challenge activity 3.4.2: set operations with three sets. 664492.400298…
For the first problem (\(\overline{A}\)): The region is the part of the universal set outside of circle \(A\) (the non - overlapping part of \(B\) and the part of \(U\) outside bo…
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point s is located at (1, -5) on the coordinate plane. point s is refle…
$(-1,5)$
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point m is located at (-4, 4) on the coordinate plane. point m is refle…
$(4,-4)$
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point s is located at (1, 1) on the coordinate plane. point s is reflec…
$S'(-1,1)$
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problem 10: spiral review determine the exact length of the unlabeled s…
$\sqrt{65}$
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choose the poem that uses trochaic meter. and oft some distant tinkling…
The lines from William Shakespeare's "Macbeth": "Double, double toil and trouble; Fire burn and caldron bubble. Cool it with a baboon's blood, Then the charm is firm and good."
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question 2 consider the graph of the line. in order to draw this line, …
C. 1
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engaged citizenship requires electoral participation political awarenes…
Question 1: D. all of the above Question 2: D. all of the above
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find the length of the three missing sides in the rhombus below. answer…
\(x = 75\), \(y = 75\), \(z = 75\)
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write the equation of the line in fully simplified slope - intercept fo…
$y=x - 5$
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the conjecture stating that vertical angles are congruent is called the
Vertical Angles Theorem
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the conjecture stating that alternate interior angles between two paral…
1. Alternate Interior Angles Conjecture 2. Corresponding Angles Conjecture 3. Consecutive Interior Angles Conjecture
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read the passage from sugar changed the world. if you walked down beekm…
"Simple enough; but this trade up and down the Atlantic coast was part of a much larger world system."
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observe the series of transformations below. what is the series of tran…
Rotation of $90^{\circ}$ clockwise about the origin and a translation of 6 units down.
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angles that are on the same side of a transversal and between two paral…
1. Consecutive interior angles 2. Transversal 3. Perpendicular bisector
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question 3 justin and carolina are working on triangle jkls transformat…
Translation, then reflection ### Question 4
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question 1 △abc has vertices (-3, 4), (-7, 8), and (-5, 2). △abc is ref…
Question 1: A. $(-3,-4)$ Question 2: D. $(1,-3)$
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directions: for the following questions, choose the best answer or resp…
1. A. The wall will lead to a violent and inhumane result. 2. B. "There would be no way out, only a struggle getting bloodier and bloodier, a deeper and sharper hooking and tearin…
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read the passage from sugar changed the world. textbooks talk about the…
"Beekman's trade, for example, could cut out Europe entirely."
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two angles that are opposite each other when two lines intersect are ca…
1. Vertical angles 2. Alternate - interior angles 3. Corresponding angles
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which of the following series of transformations could govern the trans…
A rotation 90° clockwise followed by a translation down.
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find the measure of the missing angles. answer attempt 2 out of 5 x = y…
$x = 64$, $y = 90$
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according to the alternate interior angles conjecture, if parallel line…
A. 75°
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according to the corresponding angles conjecture, if parallel lines ( l…
C. 95°
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in parallelogram abcd, diagonals ac and bd intersect at point e. if ∠da…
B. \(75^{\circ}\)
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if two parallel lines are cut by a transversal, what can be said about …
c. They are congruent.
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read the passage from sugar changed the world. one of these early hindu…
"sugar cane was now an ingredient in ceremonies involving fire", "Perhaps that transformation itself seemed magical", "sugar cane is called ikshu, which means 'something that peop…
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according to the alternate interior angles conjecture, if parallel line…
C. $90^{\circ}$
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7. when triangle abc is reflected across line ab, the image is triangle…
A. Corresponding parts of congruent figures are congruent.
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read the passage from sugar changed the world. one of these early hindu…
Hindus who lived in ancient times believed that sugar had powerful properties.
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hexagon l is a scaled copy of hexagon k. what is the value of j?
$3.3$
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triangle e is a scaled copy of triangle d. what is the value of f? 1.6 …
$2.4$
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pentagon i is a scaled copy of pentagon h. what is the value of j?
15
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in progress check for understanding: rotations not graded directions an…
$(-y,x)$