Question

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dilate \\( \triangle j k l \\) by a scale factor of \\( \frac { 1 } { 3 } \\) with the center of dilation at the origin.

Explanation:

Step1: Find coordinates of \(J\), \(K\), \(L\)

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

Step2: Apply dilation formula

The formula for dilation with center at the origin \((x,y)\to(kx,ky)\), where \(k = \frac{1}{3}\)
For \(J(-9,6)\):
\(x'=\frac{1}{3}\times(-9)= - 3\), \(y'=\frac{1}{3}\times6 = 2\), new point \(J'(-3,2)\)
For \(K(0,9)\):
\(x'=\frac{1}{3}\times0 = 0\), \(y'=\frac{1}{3}\times9=3\), new point \(K'(0,3)\)
For \(L(-6,0)\):
\(x'=\frac{1}{3}\times(-6)=-2\), \(y'=\frac{1}{3}\times0 = 0\), new point \(L'(-2,0)\)

Answer:

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