Question

AB has endpoints A(2,9) and B(5,8). A dilation, centered at the origin, is applied to AB. The image has endpoints A' (4/3,6) and B'(10/3,16/3). ​

Answer 1

Answer:

scale factor = $\frac{2}{3}$

Step-by-step explanation:

To determine the scale factor calculate the ratio of image coordinates to corresponding original coordinates, that is

Given A(2, 9 ) → A'($\frac{4}{3}$, 6 )

scale factor = $\frac{6}{9}$ = $\frac{2}{3}$ ← using y- coordinates

scale factor = $\frac{\frac{4}{3} }{2}$ = $\frac{2}{3}$ ← using the x- coordinates

The same scale factor is applied to B(5, 8 ) → B'( $\frac{10}{3}$, $\frac{16}{3}$ )