Question 7

Question

Plot and state the points of your new house from Chapter 2 after a counterclockwise rotation of 180 degrees about the origin. Use a different color to plot the points. Name the new coordinates and color you used on your graph here.
Question 8
Is the new location of your house after this transformation congruent to the neighbor’s house in Chapter 3? Explain your answer.

Answer 1

Question 7:

To perform a counterclockwise rotation of 180 degrees about the origin, we will multiply each coordinate of the points of the new house by -1.

Let's assume the coordinates of the points of the new house are as follows:
- Point A: (x1, y1)
- Point B: (x2, y2)
- Point C: (x3, y3)

After a counterclockwise rotation of 180 degrees about the origin, the new coordinates will be:
- Point A: (-x1, -y1)
- Point B: (-x2, -y2)
- Point C: (-x3, -y3)

Let's use a different color, red, to plot the new points on the graph.

Question 8:

To determine if the new location of your house after the rotation transformation is congruent to the neighbor's house, we need to compare the distances and angles between the corresponding points of both houses.

If the distances between corresponding points of both houses remain the same and the angles between lines connecting corresponding points are congruent, then the houses are congruent. However, without additional information about the neighbor's house in Chapter 3, we cannot determine if the rotation transformation makes your house congruent to the neighbor's house.