Final answer:
To determine the coordinates of △X'Y'Z' after a 90° counterclockwise rotation, apply the transformation x' = -y and y' = x to each vertex of △XYZ.
Step-by-step explanation:
When you rotate triangle XYZ by 90° counterclockwise about the origin, the coordinates of the triangle's vertices change according to a specific rule: The new x-coordinate becomes the negative of the old y-coordinate, and the new y-coordinate becomes the old x-coordinate. This transformation can be summarized by the formulas x' = -y and y' = x. Applying this to triangle XYZ: For point X, if the original coordinates are (x, y), the new coordinates will be (-y, x). For point Y, if the original coordinates are (x, y), the new coordinates will be (-y, x). For point Z, if the original coordinates are (x, y), the new coordinates will be (-y, x). Therefore, to find the coordinates of △X'Y'Z', you would apply the rotation formulas to each vertex point of the original triangle XYZ.