Question

What are the vertices of A'B'C if ABC is dilated by a scale factor of 1/2?

a. A' (32, 0), B' (48, 24), C' (24, 32)
b. A' (8, 0), B' (12, 6), C' (6, 8)
c. A' (16, 0), B' (24, 6), C' (12, 8)
d. A' (8, 0), B' (12, 12), C' (6, 16)

Answer 1

To dilate a figure by a scale factor of 1/2, each vertex is multiplied by the scale factor. The correct coordinates for A', B', and C' are (16, 0), (24, 6), and (12, 8) respectively.

Step-by-step explanation:

To dilate a figure, each vertex is multiplied by the scale factor. In this case, the scale factor is 1/2. Let's apply the scale factor to the coordinates of ABC:

Vertex A' = (1/2 * x-coordinate of A, 1/2 * y-coordinate of A)

Vertex B' = (1/2 * x-coordinate of B, 1/2 * y-coordinate of B)

Vertex C' = (1/2 * x-coordinate of C, 1/2 * y-coordinate of C)

Using this formula, we can calculate the coordinates of A', B', and C'. The correct answer is option c. A' (16, 0), B' (24, 6), and C' (12, 8).