Question

Triangle ABC ​is transformed with the center of dilation at the origin.

Pre-image: △ABC with vertices A(−5, −4), B(−7, 3), C(3, −2)

Image: △A′B′C′ with vertices A′(−3.75, −3), B′(−5.25, 2.25), C′(2.25, −1.5)



What is the scale factor of the dilation that maps the pre-image to the image?

Enter your answer in the box. Your answer must be a fraction, reduced to lowest terms.

Answer 1

Dilation is a transformation that maps an object to an image by stretching or diminishing it but retaining the original shape. It is described by stating the center of dilation and the dilation scale factor.
Dilation scale factor is given by dividing the coordinate of the image with the corresponding coordinate of the object.
In this case, if we consider A and A' then; k(-5,-4) = (-3.75, -3)
Thus, -5k = -3.75 or -4k = -3
          k = 3/4
Hence the scale factor of dilation is 3/4