Question

Because you are famous, people want to live near you. You have a new neighbor move in across the street after they build the same exact house as you did in Chapter 3.
Question 7
With a different color, plot and state the points of your neighbor’s house, which is a reflection of your house in Chapter 3 over the y-axis. Name the color you use on your graph here.
Question 8
Is your new house after this transformation congruent to the house in Chapter 3? Explain your answer.

Answer 1

I don’t have the actual coordinates of your Chapter 3 house. If you paste those points I will compute and plot the reflection for you.

Meanwhile here is how to do it and a short example:

How to reflect over the y-axis
- Rule: (x, y) → (−x, y).
- So for each vertex of your house, change the sign of the x-coordinate and keep the y-coordinate the same.
- On your graph use a different color than the original; I’ll say “red” for the neighbor’s house.

Example (original house vertices)
- Suppose the house in Chapter 3 has vertices: (1,1), (4,1), (4,4), (1,4) for the rectangle and (2.5,5.5) for the roof peak.

Reflected (neighbor’s) vertices over the y-axis (in red)
- (1,1) → (−1,1)
- (4,1) → (−4,1)
- (4,4) → (−4,4)
- (1,4) → (−1,4)
- (2.5,5.5) → (−2.5,5.5)

Plotting note
- Plot the reflected points in red, then connect them in the same order you did the original house so the shape and roof appear properly.

Question 8 — Are the two houses congruent?
- Yes. A reflection across the y-axis is a rigid motion (an isometry): it preserves distances and angles. The reflected house has the same side lengths and angles as the original, only mirrored, so it is congruent.

If you give the exact Chapter 3 coordinates, I’ll produce the exact reflected points and label the color you want.