Question 7
To plot the points of your neighbor’s house as a reflection over the y-axis, you will take each of your original house's points (let's assume they are \( (x, y) \)) and transform them to their new coordinates as \( (-x, y) \).
For example, if the points of your house in Chapter 3 are:
- \( A(1, 2) \)
- \( B(3, 4) \)
- \( C(5, 2) \)
Then the reflected points of your neighbor's house would be:
- \( A'(-1, 2) \)
- \( B'(-3, 4) \)
- \( C'(-5, 2) \)
You could use purple to plot these points on your graph.
Question 8
Yes, your new house, after reflecting over the y-axis, is congruent to the house in Chapter 3. Congruent shapes are identical in size and shape but may be in different positions or orientations. Since the reflection preserves the distances and angles, the shapes are congruent.
Now, let's plot and state the points of your original house after a counterclockwise rotation of 180 degrees about the origin. To do this transformation, you change each point \( (x, y) \) to \( (-x, -y) \).
Using the previous example, the transformed points after a 180-degree rotation would be:
- \( A(1, 2) \rightarrow A''(-1, -2) \)
- \( B(3, 4) \rightarrow B''(-3, -4) \)
- \( C(5, 2) \rightarrow C''(-5, -2) \)
You could use green to plot these points on your graph.
Summary of Points
-
Neighbor's house (reflection over the y-axis):
- \( A'(-1, 2) \) (purple)
- \( B'(-3, 4) \)
- \( C'(-5, 2) \)
-
Your house after rotation:
- \( A''(-1, -2) \) (green)
- \( B''(-3, -4) \)
- \( C''(-5, -2) \)
Make sure to clearly label each set of points in your graph according to their respective transformations and colors!