Question

dilate △jkl by a scale factor of 1/3 with the center of dilation at the origin.

Explanation:

Step1: Find the coordinates of the original points

From the graph, \(J(-9,7)\), \(K(0,9)\), \(L(-6,0)\)

Step2: Apply the dilation formula

The formula for dilation with center at the origin \((x,y)\to(kx,ky)\), where \(k = \frac{1}{3}\)
For point \(J\):
\(x=-9,y = 7\)
\(x'=\frac{1}{3}\times(-9)=-3\), \(y'=\frac{1}{3}\times7=\frac{7}{3}\)
New coordinates \(J'(-3,\frac{7}{3})\)
For point \(K\):
\(x = 0,y=9\)
\(x'=\frac{1}{3}\times0 = 0\), \(y'=\frac{1}{3}\times9 = 3\)
New coordinates \(K'(0,3)\)
For point \(L\):
\(x=-6,y = 0\)
\(x'=\frac{1}{3}\times(-6)=-2\), \(y'=\frac{1}{3}\times0=0\)
New coordinates \(L'(-2,0)\)

Answer:

The coordinates of the dilated triangle \(\triangle J'K'L'\) are \(J'(-3,\frac{7}{3})\), \(K'(0,3)\), \(L'(-2,0)\)