Question

If Δabc is reflected over the y-axis and then dilated by a scale factor of 3 about the origin, where are the vertices of Δa'b'c' located?

1) (3,3), (1, 2), and (0,4)
2) (6, 6), (2, 4), and (0, 8)
3) (9, 9), (3, 6), and (0, 12)
4) (-9, -9), (-3, -6), and (0, -12)

Answer 1

The vertices of Δa'b'c' are located at (-9, 9), (-3, 6), and (0, 12) after being reflected over the y-axis and dilated by a scale factor of 3 about the origin.

Step-by-step explanation:

To find the vertices of the reflected and dilated triangle, we need to apply both transformations to each vertex of the original triangle.

First, reflect each vertex over the y-axis. This means changing the sign of the x-coordinate for each vertex.

• For vertex A, (3, 3), the reflected vertex is (-3, 3).
• For vertex B, (1, 2), the reflected vertex is (-1, 2).
• For vertex C, (0, 4), the reflected vertex is (0, 4).

Next, dilate each reflected vertex about the origin by a scale factor of 3. This means multiplying both the x-coordinate and y-coordinate by 3.

• For vertex A', (-3, 3), the dilated vertex is (-9, 9).
• For vertex B', (-1, 2), the dilated vertex is (-3, 6).
• For vertex C', (0, 4), the dilated vertex is (0, 12).

Therefore, the vertices of Δa'b'c' are located at (-9, 9), (-3, 6), and (0, 12) (Option 3).