Angle ABC contains the points A (-5,3), B(-4,-2), and C (1,4). Describe the effect of the dilation of the angle with a scale factor of 8 and a center of dilation at the origin (0,0).

Answer 1

A dilation with a scale factor of 8 and a center of dilation at the origin (0,0) will stretch all points in the angle away from the origin by a factor of 8.

Let's find the coordinates of the image points:

Image of A = (-5×8, 3×8) = (-40, 24)
Image of B = (-4×8, -2×8) = (-32, -16)
Image of C = (1×8, 4×8) = (8, 32)

Therefore, the image of angle ABC, denoted as angle A'B'C', has the points A' (-40, 24), B' (-32, -16), and C' (8, 32).