Question

The vertices of a triangle are located at F(-4, -2), G(2, 2), and H(0, -4). A sequence of transformations to triangle FGH results in triangle F'G'H', as shown below.

Answer 1

A sequence of transformations to triangle FGH results in triangle F'G'H' include the following: D. a 90º clockwise rotation about the origin, then a dilation by a scale factor of 1 half with a center of dilation at the origin.

In Mathematics and Geometry, the rotation of a point 90° about the center (origin) in a clockwise direction would produce a point that has these coordinates (y, -x).

By applying a rotation of 90° clockwise about the center (origin), the coordinates of triangle A'B'C' are as follows;

(x, y) → (y, -x)

Coordinate F (-4, -2) → Coordinate F' (-2, 4)

Coordinate G (2, 2) → Coordinate G' (2, -2)

Coordinate H (0, -4) → Coordinate H' (-4, 0)

Next, we would dilate the new triangle by a scale factor of 1/2;

Coordinate F' (-2, 4) → (-2 × 1/2, 4 × 1/2) = F" (-1, 2).

Coordinate G' (2, -2) → (2 × 1/2, -2 × 1/2) = G" (1, -1).

Coordinate H' (-4, 0) → (-4 × 1/2, 0 × 1/2) = H" (-2, 0).