unit 1 assessmentstudent instructions: you may use a straightedge, tracing paper, and your reference chart.1. draw triangle a after the translation $(x,y)\to(x + 1, y - 3)$. label the new triangle b.2. draw triangle a after it has been reflected over the y-axis. label the new triangle c.3. draw triangle a after it has been rotated $90^\circ$ clockwise about the origin. label the new triangle d.4. draw triangle a after it has been reflected over the line $y=-2$. label the new triangle e.5. a regular hexagon has how many lines of symmetry?a) no reflection symmetryb) exactly 3 lines of symmetryc) exactly 6 lines of symmetry6. what is the angle of rotation for a regular hexagon?d) no rotational symmetrye) $60^\circ$ rotational symmetryf) $90^\circ$ rotational symmetry7. find $m\angle wzx$. show all work, and describe (in words) what you did to find it.8. given that lines x and y are parallel. which of the following represents the relationship between $\angle b$ and $\angle e$?a. $m\angle b=m\angle e$b. $m\angle b+m\angle e=180$c. $m\angle b+m\angle e=90$d. $m\angle b+m\angle e=60$

Question

Accepted Answer

### Questions 1-4 (Transformations)
First, identify the vertices of Triangle A from the grid:
- Vertex 1: $(0, 1)$
- Vertex 2: $(2, 3)$
- Vertex 3: $(-4, 1)$

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#### 1. Translation $(x,y)	o(x+4, y-3)$
# Explanation:
## Step1: Translate each vertex
New Vertex 1: $(0+4, 1-3)=(4, -2)$
New Vertex 2: $(2+4, 3-3)=(6, 0)$
New Vertex 3: $(-4+4, 1-3)=(0, -2)$
## Step2: Plot & label Triangle B
Connect $(4,-2)$, $(6,0)$, $(0,-2)$ on the grid.
# Answer:
Triangle B has vertices $(4, -2)$, $(6, 0)$, $(0, -2)$ (plot these points and connect to form the triangle).

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#### 2. Reflection over y-axis
# Explanation:
## Step1: Reflect each vertex
Rule: $(x,y)	o(-x,y)$
New Vertex 1: $(0, 1)$ (unchanged, on y-axis)
New Vertex 2: $(-2, 3)$
New Vertex 3: $(4, 1)$
## Step2: Plot & label Triangle C
Connect $(0,1)$, $(-2,3)$, $(4,1)$ on the grid.
# Answer:
Triangle C has vertices $(0, 1)$, $(-2, 3)$, $(4, 1)$ (plot these points and connect to form the triangle).

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#### 3. 90° clockwise rotation about origin
# Explanation:
## Step1: Rotate each vertex
Rule: $(x,y)	o(y,-x)$
New Vertex 1: $(1, 0)$
New Vertex 2: $(3, -2)$
New Vertex 3: $(1, 4)$
## Step2: Plot & label Triangle D
Connect $(1,0)$, $(3,-2)$, $(1,4)$ on the grid.
# Answer:
Triangle D has vertices $(1, 0)$, $(3, -2)$, $(1, 4)$ (plot these points and connect to form the triangle).

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#### 4. Reflection over $y=-2$
# Explanation:
## Step1: Calculate vertical distance to line
For a point $(x,y)$, distance to $y=-2$ is $|y - (-2)|=|y+2|$. New y-coordinate: $-2 - (y+2)=-y-4$
## Step2: Find new vertices
New Vertex 1: $(0, -1-4)=(0, -5)$
New Vertex 2: $(2, -3-4)=(2, -7)$
New Vertex 3: $(-4, -1-4)=(-4, -5)$
## Step3: Plot & label Triangle E
Connect $(0,-5)$, $(2,-7)$, $(-4,-5)$ on the grid.
# Answer:
Triangle E has vertices $(0, -5)$, $(2, -7)$, $(-4, -5)$ (plot these points and connect to form the triangle).

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### Question 5
# Brief Explanations:
A regular hexagon has 6 equal sides, so it has 6 lines of symmetry (3 through opposite vertices, 3 through midpoints of opposite sides).
# Answer:
c) Exactly 6 lines of symmetry

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### Question 6
# Brief Explanations:
Rotational symmetry angle = $\frac{360^\circ}{	ext{number of sides}}$. A regular hexagon has 6 sides, so $\frac{360^\circ}{6}=60^\circ$.
# Answer:
e) $60^\circ$ rotational symmetry

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### Question 7
# Explanation:
## Step1: Identify vertical angles
$m\angle YXZ = 70^\circ$ (vertical angle to the given $70^\circ$ angle)
## Step2: Use triangle angle sum
Sum of angles in $	riangle WZX$ is $180^\circ$.
$m\angle WZX = 180^\circ - 70^\circ - 35^\circ$
## Step3: Calculate the angle
$180 - 70 - 35 = 75$
# Answer:
$m\angle WZX = 75^\circ$
Explanation: First, identify the vertical angle to the given $70^\circ$ angle, which is also $70^\circ$. Then subtract this angle and the given $35^\circ$ angle from $180^\circ$ (the total sum of angles in a triangle) to find the missing angle.

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### Question 8
# Brief Explanations:
When two parallel lines are cut by a transversal, same-side interior angles are supplementary (sum to $180^\circ$). $\angle b$ and $\angle e$ are same-side interior angles.
# Answer:
b. $m\angle b + m\angle e = 180$

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QUESTION IMAGE

Question

Explanation:

Questions 1-4 (Transformations)

1. Translation $(x,y)\to(x+4, y-3)$

Step1: Translate each vertex

Step2: Plot & label Triangle B

Step1: Reflect each vertex

Step2: Plot & label Triangle C

Step1: Rotate each vertex

Step2: Plot & label Triangle D

Answer:

2. Reflection over y-axis