Question

Triangle XYZ with vertices X(4, -1), Y(8,-2), and Z(1, -8) is rotated 180° about the origin. What is the y-coordinate of Z'?.

Answer 1

The y-coordinate of Z' after a 180° rotation about the origin is 8.

Step-by-step explanation:

When triangle XYZ with vertices X(4, -1), Y(8,-2), and Z(1, -8) is rotated 180° about the origin, the coordinates of each point are negated. This is because a 180° rotation is equivalent to reflecting a point over both the x-axis and the y-axis. Therefore, the y-coordinate of Z after the rotation, which we'll call Z' (-1, 8), will simply be the negative of the original y-coordinate. So, the y-coordinate of Z' is 8.