Question

17 dilate triangle ijk center of dilation: (0, 0) scale factor: $\frac{2}{3}$ i: __________ j: ________ k: __________

Explanation:

Step1: Identify the coordinates of points I, J, K

Assume from the grid, I = (-6,-4), J=(6,2), K = (-6,-8).

Step2: Apply the dilation formula

The formula for dilation with center (0,0) is (x',y')=(kx,ky) where k is the scale - factor. Here k = $\frac{2}{3}$.
For point I:
$x_{I'}=\frac{2}{3}\times(-6)=-4$
$y_{I'}=\frac{2}{3}\times(-4)=-\frac{8}{3}$
So I'=$(-4,-\frac{8}{3})$
For point J:
$x_{J'}=\frac{2}{3}\times6 = 4$
$y_{J'}=\frac{2}{3}\times2=\frac{4}{3}$
So J'=$(4,\frac{4}{3})$
For point K:
$x_{K'}=\frac{2}{3}\times(-6)=-4$
$y_{K'}=\frac{2}{3}\times(-8)=-\frac{16}{3}$
So K'=$(-4,-\frac{16}{3})$

Answer:

I': $(-4,-\frac{8}{3})$
J': $(4,\frac{4}{3})$
K': $(-4,-\frac{16}{3})$