Question

Triangle abc is shown on the coordinate plane. a triangle on the coordinate plane with vertices a at (-3, 3), b at (-1, 2), and c at (0, 4). 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 triangle A'B'C' would be (9, 9), (3, 6), and (0, 12).

Step-by-step explanation:

To reflect a point over the y-axis, we change the sign of its x-coordinate.

So, the new coordinates of point A' would be (3, 3) since the x-coordinate (-3) becomes positive.

To dilate a point by a scale factor of 3, we multiply both coordinates by 3.

So, the new coordinates of point A'' would be (9, 9) since we multiplied both the x-coordinate and y-coordinate of A' by 3.

Similarly, for points B and C, we follow the same process to find the coordinates of B' and C', and then multiply both coordinates by 3 to find the coordinates of B'' and C''.

The vertices of triangle A'B'C' would be (9, 9), (3, 6), and (0, 12).