Question

Triangle CAT is graphed on a coordinate grid with vertices at C(-3, -6), A(0, 3), and T(6, -3). Triangle CAT is dilated by a scale factor of p with the origin as the center of dilation to create triangle C’A’T’. Which ordered pair represents the coordinates of the vertex T’?

a) (6+p, −3+p)
b) (6p, −3p)
c) (6p, −3p)
d) (6−p, −3−p)

Answer 1

The coordinates of vertex T' after the dilation with a scale factor of p with origin as the center are (6p, -3p), which corresponds to option (b).

Step-by-step explanation:

The question involves dilating a triangle on a coordinate grid. Triangle CAT is being dilated by a scale factor of p. To find the coordinates of vertex T' after the dilation, we need to multiply each coordinate of T by p because the dilation is centered at the origin. Therefore, the original coordinates of T(6, -3) become (6p, -3p) after the dilation. Hence, the correct answer is (b) (6p, -3p).