Question

Describe the effect of the dilation of the angle D (2,4), E (2,1), F (3,-3), with a scale factor of 4 and a center point of dilation at the origin (0,0).

Answer 1

Dilation is a transformation that resizes or enlarges a shape in a certain ratio from a fixed center point. In this case, the dilation of angle DEF with a scale factor of 4 means that each point of the angle will be moved four times farther from the origin while maintaining the same angle measurement.

Given the points D(2,4), E(2,1), and F(3,-3), if we multiply the x and y coordinates of each point by 4, we can calculate the new coordinates after the dilation:

Point D:
x-coordinate: 2 * 4 = 8
y-coordinate: 4 * 4 = 16

So, the new coordinate for point D after dilation is D'(8, 16).

Point E:
x-coordinate: 2 * 4 = 8
y-coordinate: 1 * 4 = 4

The new coordinate for point E after dilation is E'(8, 4).

Point F:
x-coordinate: 3 * 4 = 12
y-coordinate: -3 * 4 = -12

Thus, the new coordinate for point F after dilation is F'(12, -12).

Therefore, the angle D'E'F' is dilated from the original angle DEF with a scale factor of 4 and a center point of dilation at the origin (0,0).