Question

Consider the polygon GOEM with coordinates G(0, -2), E(-1, 2), O(-5, 1), M(-5, -6). If we rotate GOEM 90° clockwise about the origin, then reflect over the y-axis, what are the coordinates of G''O''E''M''?

a) G''(-2, 0), O''(1, -5), E''(2, -1), M''(-6, -5)
b) G''(2, 0), O''(1, 5), E''(-2, 1), M''(-6, 5)
c) G''(2, 0), O''(-1, -5), E''(-2, -1), M''(6, -5)
d) G''(-2, 0), O''(-1, 5), E''(2, 1), M''(6, 5)

Answer 1

The coordinates of G''O''E''M'' after rotating 90° clockwise about the origin and reflecting over the y-axis are a) G''(-2, 0), O''(-1, -5), E''(2, -1), M''(6, -5).

Step-by-step explanation:

To rotate a point 90° clockwise about the origin, the x-coordinate becomes the y-coordinate and the y-coordinate becomes the negative of the x-coordinate. Applying this transformation to each point in the polygon GOEM, we get G'(2, 0), E'(-2, -1), O'(1, -5), and M'(-6, -5).

To reflect a point over the y-axis, we change the sign of the x-coordinate. Applying this transformation to each point, we get G''(-2, 0), E''(2, -1), O''(-1, -5), and M''(6, -5).

The correct coordinates for G''O''E''M'' are (a) G''(-2, 0), O''(-1, -5), E''(2, -1), M''(6, -5)