Question

A dilation has center (0, 0). Find the image of each point for the given scale factor. M(-2, 4), Dilation with scale factor 4

Answer 1

The image of point M(-2, 4) after a dilation with center (0, 0) and scale factor of 4 is M'(-8, 16), obtained by multiplying both coordinates of M by the scale factor.

Step-by-step explanation:

To find the image of the point M(-2, 4) under a dilation with a scale factor of 4 and center (0, 0), you would multiply both the x-coordinate and the y-coordinate of M by the scale factor. Here is the step-by-step calculation:

1. Identify the coordinates of point M, which are (-2, 4).
2. Identify the scale factor for the dilation, which is 4.
3. Multiply the x-coordinate of M (-2) by the scale factor (4) to get the x-coordinate of the image, which is -2 * 4 = -8.
4. Multiply the y-coordinate of M (4) by the scale factor (4) to get the y-coordinate of the image, which is 4 * 4 = 16.
5. The coordinates of the image of M after the dilation are (-8, 16).

Therefore, the image of point M(-2, 4) after the dilation with a center at the origin (0,0) and a scale factor of 4 is M'(-8, 16).