Determine the scale factor used in the dilation of line segment AB, with a center point of dilation at the origin. (1 point)
To determine the scale factor used in the dilation of line segment AB with a center point of dilation at the origin, we need to compare the coordinates of point A and point B before and after the dilation.
Let's assume point A has coordinates (x1, y1) and point B has coordinates (x2, y2) before the dilation. After the dilation, let's say point A' has coordinates (kx1, ky1) and point B' has coordinates (kx2, ky2), where k is the scale factor.
Since the center point of dilation is the origin (0, 0), the formula for dilation can be written as:
A' = k * A
B' = k * B
By dividing the coordinates of point B' by point A' we can eliminate the k:
(kx2, ky2) / (kx1, ky1) = (x2, y2) / (x1, y1)
Solving for k:
k = sqrt((x2^2 + y2^2)/(x1^2 + y1^2))
Thus, the scale factor used in the dilation of line segment AB is the square root of the ratio of the squares of the coordinates of point B to point A.