Question

Dilate using a scale factor of 1/3, then reflect over the y-axis.

(-30, 12), (-30, -24), (0, -24), (-18, -12)
a) (-10, 4), (10, 24), (0, 24), (6, 12)
b) (-10, 4), (10, -8), (0, -8), (6, -4)
c) (-30, 4), (-30, -8), (0, -8), (-18, -4)
d) (-10, 4), (10, -24), (0, -24), (6, -12)

Answer 1

After dilating each point by a scale factor of 1/3 and reflecting over the y-axis, the transformed set of points is option b) (-10, 4), (10, -8), (0, -8), (6, -4).

Step-by-step explanation:

The question involves performing two geometric transformations on a set of points in the coordinate plane: a dilation with a scale factor and a reflection over the y-axis. First, we need to dilate each point by a scale factor of 1/3, which means multiplying each coordinate (x, y) by 1/3. Then, we need to reflect the resulting points over the y-axis, which means changing the sign of the x-coordinate of each point. Let's perform these steps for each point:

• Dilate (-30, 12) by 1/3 to get (-10, 4), then reflect over the y-axis to get (10, 4).
• Dilate (-30, -24) by 1/3 to get (-10, -8), then reflect over the y-axis to get (10, -8).
• Dilate (0, -24) by 1/3 to get (0, -8), then reflect over the y-axis, which does not change the point because it's already on the y-axis, so it remains (0, -8).
• Dilate (-18, -12) by 1/3 to get (-6, -4), then reflect over the y-axis to get (6, -4).

Therefore, the correct answer is (b) (-10, 4), (10, -8), (0, -8), (6, -4).