1. The problem is to find the image of triangle ABC after a 270° clockwise rotation about the origin. 2. The formula for a 270° clockwise rotation (which is equivalent to a 90° counterclockwise rotation) about the origin is: $$ (x, y) \to (y, -x) $$ This means each point's new coordinates are found by swapping the original coordinates and negating the new y-coordinate. 3. Suppose the vertices of triangle ABC are: $$ A(x_1, y_1), B(x_2, y_2), C(x_3, y_3) $$ Applying the rotation to each vertex: $$ A' = (y_1, -x_1) $$ $$ B' = (y_2, -x_2) $$ $$ C' = (y_3, -x_3) $$ 4. For example, if vertex A is at (1, 7), then: $$ A' = (7, -1) $$ 5. This transformation preserves the shape and size of the triangle but changes its orientation and position according to the rotation. 6. To summarize, the rotated triangle ABC after 270° clockwise rotation about the origin has vertices: $$ A'(y_1, -x_1), B'(y_2, -x_2), C'(y_3, -x_3) $$ This completes the solution.