Parallelogram JKLM has vertices J(-1, 6), K(0, 9), L(6, −3), and M(3, −3). What is the coordinates of the image if the parallelogram is dilated with a scale factor of -1/3

Question

asked Feb 11, 2021 181k views

1 Answer

Hongbin Wang · Answer 1 · 2021-02-16T21:34:53+0000

Answer:
$(\frac13,-2),\ (0,-3),\ (-2,1),\ (-1,1) .$

Explanation:

Transformation rule for dilation:

$(x,y)\to(kx,ky)$ , where k = scale factor

Given : Scale factor =
$-\frac13$

Parallelogram JKLM has vertices J(-1, 6), K(0, 9), L(6, −3), and M(3, −3)

Vertices after dilation:

$(-1,6)\to(-1*(-1)/(3),6*(-1)/(3))=(\frac13,-2)$

$(0,9)*(0*-\frac13,9*-\frac13)=(0,-3)$

$(6,-3)\to(6*-\frac13,\ -3*-\frac13)=(-2,1)$

$(3,-3)\to (3*-\frac13,\ -3*-\frac13)=(-1,1)$

Hence, the coordinates of the image if the parallelogram =
$(\frac13,-2),\ (0,-3),\ (-2,1),\ (-1,1) .$