Question

Q(3, -6) R(3, 12) S(12, 3) ----> Q'(1, -2) R'(1,4) S'(4,1) QRS is dilated to form Triangle Q'R'S'. By the given coordinate points, what scale factor was used to form Triangle Q'R'S'?

Answer 1

Answer: Scale factor =
`(1)/(3)`

Explanation: In a dilation, a geometric figure can be bigger or smaller than the original. In the case of triangles QRS and Q'R'S', the second is smaller than the first.

This means, the scale factor which forms triangle Q'R'S' is a fraction.

Comparing Q and Q', we noticed that Q' is a 3rd of Q, i.e.:

Q(3,-6)

x = 3

y = 6

x' =
`(3)/(3)` = 1

y'=
`(-6)/(3)` = -2

Therefore, the scale factor used to form triangle Q'R'S' is
`(1)/(3)`