Question

The composition D Subscript 0, three-halves (x, y) is a composition of D Subscript 0, one-half (x, y) is applied to △RST to create the image of △R"S"T", which is not shown.

On a coordinate plane, triangle R S T has points (negative 6, 10), (negative 2, 6), and (negative 10, 0).

What are the coordinates of point S"?

(negative three-halves, nine-halves)
(negative nine-halves, fifteen-halves)
(nine-halves, negative three-halves)
(negative fifteen-halves, 0)

Answer 1

Scale factors multiply under composition. The composite dilation about the origin has factor (1/2)*(3/2) = 3/4.

S = (−2, 6) → S" = (−2*(3/4), 6*(3/4)) = (−3/2, 9/2).

So the correct choice is (−3/2, 9/2).