Question

A rectangle has vertices J(3, 3), K(9, 3), L(9, 6), and M(3, 6). Give the coordinates after dilating from the origin by a scale factor of 2/3.

Answer 1

J'(2,2) , K'(6,2), L'(6,4) and M'(2,4)

Explanation:

Given:

The coordinates of the rectangle are:

J(3, 3), K(9, 3), L(9, 6), and M(3, 6)

The scale factor is 2/3

New coordinates = ?

Multiplying the coordinates by 2/3 to find the vertices of the image

$J(3, 3) = J' (\frac{2}{3} . 3 , \frac{2}{3} . 3) = J' (2,2)\\\\K(9, 3) = K' (\frac{2}{3} . 9 , \frac{2}{3} . 3) = K' (6,2)\\\\L(9, 6) = L' (\frac{2}{3} . 9 , \frac{2}{3} . 6) = L' (6,4)\\\\M(3, 6) = M'(\frac{2}{3} . 3 , \frac{2}{3} . 6) = M' (2,4)$

The vertices of the image are:

J'(2,2) , K'(6,2), L'(6,4) and M'(2,4)