Question

Quadrilateral GHJK has vertices G(2, 3), H(8, 2), J(6, 8), and K(3,6). It is transformed according to the rule T(-4,-5) ° Ro, 270°. What are the coordinates of G"?

a) (-7, 3)
b) (-2, 2)
c) (-1, -7)
d) (2, -2)

Answer 1

After applying the transformation T(-4, -5) and a 270-degree rotation, the coordinates of point G" are (-2, 2), which is option (b).

Step-by-step explanation:

The question asks us to find the coordinates of the transformed point G" after applying the transformation T(-4, -5) ° R0, 270° to quadrilateral GHJK with given vertices. This involves a translation followed by a 270-degree rotation about the origin.

First, point G(2, 3) will be translated using T(-4, -5), which shifts the point 4 units to the left and 5 units down, resulting in G'(2 - 4, 3 - 5) = G'(-2, -2).

To then apply the 270-degree rotation, point G' will be rotated about the origin.

The rule for a 270-degree rotation (counter-clockwise) around the origin is (x, y) becomes (y, -x), which will transform G'(-2, -2) to G"(-2, 2).

Thus, the coordinates of G" are (-2, 2), which corresponds to option (b).