Question

Determine the scale factor used in the dilation of line AB , with a center point of dilation at the origin. (1 point)

A (-3,4), B (4,-8)
A' (-3,4), B' (2,-4)

Answer 1

I just need the answer

Answer 2

To find the scale factor, we can use the formula:

scale factor = length of image / length of pre-image

For line AB, the length of AB is calculated using the distance formula:

length of AB = sqrt((4 - (-3))^2 + (-8 - 4)^2) = sqrt(7^2 + (-12)^2) = sqrt(49 + 144) = sqrt(193)

For line A'B', the length of A'B' can be calculated in the same way:

length of A'B' = sqrt((2 - (-3))^2 + (-4 - 4)^2) = sqrt(5^2 + (-8)^2) = sqrt(25 + 64) = sqrt(89)

Therefore, the scale factor = length of A'B' / length of AB = sqrt(89) / sqrt(193) ≈ 0.734

Answer 3

The scale factor used in the dilation of line AB, with a center point of dilation at the origin, is approximately 0.734