Question

Triangle XYZ has vertices (picture)

Answer 1

• X'(-4, 1)
• Y'(-8, 2)
• Z'(-1, 8)

Explanation:

You want the coordinates of vertices X', Y', Z' after triangle XYZ has been rotated 180° about the origin. The original vertices are ...

• X(4, -1)
• Y(8, -2)
• Z(1, -8)

Rotation 180°

Rotation 180° about the origin will give the same result whether the direction is clockwise or counterclockwise. That same result is also obtained by reflection across the origin, or by reflection across both the x- and y-axes, in any order.

The associated coordinate transformation is ...

(x, y) ⇒ (-x, -y)

Then the coordinates for X', Y', and Z' are ...

X(4, -1) ⇒ X'(-4, 1)

Y(8, -2) ⇒ Y'(-8, 2)

Z(1, -8) ⇒ Z'(-1, 8)