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

scale factor =
`(2)/(3)`

Explanation:

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

Given A(2, 9 ) → A'(
`(4)/(3)`, 6 )

scale factor =
`(6)/(9)` =
`(2)/(3)` ← using y- coordinates

scale factor =
`((4)/(3) )/(2)` =
`(2)/(3)` ← using the x- coordinates

The same scale factor is applied to B(5, 8 ) → B'(
`(10)/(3)`,
`(16)/(3)` )