dilate $\triangle jkl$ by a scale factor of $\frac{1}{3}$ with the center of dilation at the origin.
dilate $\triangle jkl$ by a scale factor of $\frac{1}{3}$ with the center of dilation at the origin.
Answer
Explanation:
Step1: Find the coordinates of the original points
From the graph, the coordinates of (J) are ((- 8,6)), the coordinates of (K) are ((0,9)), and the coordinates of (L) are ((-6,0)).
Step2: Apply the dilation formula
The formula for dilation with a scale factor (k=\frac{1}{3}) and center at the origin ((x,y)\to(kx,ky)). For point (J(-8,6)): (x'=\frac{1}{3}\times(-8)=-\frac{8}{3}), (y'=\frac{1}{3}\times6 = 2), so the new point (J') is (\left(-\frac{8}{3},2\right)) For point (K(0,9)): (x'=\frac{1}{3}\times0 = 0), (y'=\frac{1}{3}\times9=3), so the new point (K') is ((0,3)) For point (L(-6,0)): (x'=\frac{1}{3}\times(-6)=-2), (y'=\frac{1}{3}\times0 = 0), so the new point (L') is ((-2,0))
Answer:
The coordinates of the dilated triangle (\triangle J'K'L') are (J'\left(-\frac{8}{3},2\right)), (K'(0,3)) and (L'(-2,0))