Question

AABC is dilated by a scale factor of 0.5 with the origin as the center of dilation, resulting in the image AA'B'C'. If A=(2, 2), B=(4, 3), and C= (6,3).

what is the length of B'C' ?
A. 3 units
B. 4 units
C. 2 units
D. 1 unit

Answer 1

Answer: The length of B'C' is 1 unit

Explanation:

To find the length of B'C', we need to find the coordinates of B' and C'. We can do this by applying the dilation transformation to the coordinates of B and C.

If the scale factor is 0.5 and the origin is the center of dilation, then the new coordinates (B' and C') are found by multiplying the original coordinates (B and C) by 0.5.

This means that B' is at (0.5 * 4, 0.5 * 3) = (2, 1.5) and C' is at (0.5 * 6, 0.5 * 3) = (3, 1.5). The length of B'C' is the distance between these two points, which we can find using the distance formula:

distance = sqrt((3 - 2)^2 + (1.5 - 1.5)^2)

= sqrt((1)^2 + (0)^2)

= sqrt(1)

= 1

Therefore, the length of B'C' is 1 unit