Because you are famous, people want to live near you. You have a new neighbor

Question

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

To answer your questions:

Question 7

Let’s assume the coordinates of your house (from Chapter 3) are represented by the following points:

• A(1, 2)
• B(3, 4)
• C(5, 2)

When reflecting these points over the y-axis, we negate the x-coordinates. The reflected points for your neighbor's house would be:

• A'(-1, 2)
• B'(-3, 4)
• C'(-5, 2)

For the graph, let's say you use red to plot your neighbor's house. The points A', B', and C' will be plotted in red.

Question 8

Yes, your new house (the neighbor’s house after reflection) is congruent to the house in Chapter 3. Two figures are considered congruent if they have the same shape and size, even if they are positioned differently or are mirror images of each other. The reflection over the y-axis does not change the dimensions of the house; it simply reverses its orientation. Thus, the two houses have identical lengths, widths, and angles, maintaining congruency.