Question

Line segment AB has vertices A(-3, 4) and B(1, -2). A dilation centered at the orgin is applied to AB. The image has vertices A(-1, 4/3) and B(1/3, -2/3). What is tjr scale factor of the dilation?

1. 1/6
2. 1/3
3. 3
4. 6​

Answer 1

option 2

Explanation:

consider the coordinates A (- 3, 4 ) and A' (- 1,
`(4)/(3)` )

since the dilatation is centred at the origin, then corresponding coordinates are multiples/ divisors of each other, then image to original gives scale factor.

scale factor =
`(A')/(A)` =
`(-1)/(-3)` =
`(1)/(3)` and
`((4)/(3) )/(4)` =
`(1)/(3)`

similarly B (1, - 2 ) and B' (
`(1)/(3)`, -
`(2)/(3)` )

`((1)/(3) )/(1)` =
`(1)/(3)` and
`(-(2)/(3) )/(-2)` =
`(1)/(3)`