Question

Justifying the Coordinates of a Pre-image On a coordinate plane, a line segment contains points (negative 5, 5) and (5, 0). Another segment contains points (negative 1, 1) and (1, 0). The segments shown are dilations of each other about the origin. Which statement could be true? The coordinate (1, 0) is from a dilation using the scale factor of One-fifth. The coordinate (5, 0) is from a dilation using the scale factor of 4. The coordinate (1, 0) is from a dilation using the scale factor of 5. The coordinate (5, 0) is from a dilation using the scale factor of One-fifth.

Answer 1

The coordinate (1, 0) is from a dilation using the scale factor of 5. The coordinates of the pre-image of (1, 0) are (5, 0), which is a dilation of the original point (negative 5, 5) using the scale factor of 5. This can be verified by calculating the coordinates of the pre-image using the formula (x, y) → (kx, ky).