Question

21) What are the coordinates of the image of segment CV with endpoints C(3, 2) and V (1,-6) after a dilation with scale factor 3/2 and the origin as the center of dilation?

Answer 1

The coordinates of the image of segment CV after the dilation are:

C' = (9/2, 3)

V' = (3/2, -9)

Explanation:

To perform a dilation with center of dilation at the origin and scale factor 3/2, we need to multiply the coordinates of each point by 3/2. The coordinates of point C(3, 2) become:

C' = (3 * 3/2, 2 * 3/2) = (9/2, 3)

Similarly, the coordinates of point V(1, -6) become:

V' = (1 * 3/2, -6 * 3/2) = (3/2, -9)

Therefore, the image of segment CV with endpoints C(3, 2) and V(1, -6) after the dilation with center of dilation at the origin and scale factor 3/2 is a segment with endpoints C'(9/2, 3) and V'(3/2, -9).