Question

graph the image of △klm after a dilation with a scale factor of 3, centered at the origin.

Explanation:

Step1: Recall dilation formula

For a dilation centered at the origin with scale - factor \(k\), if a point \((x,y)\) is dilated, the new point \((x',y')\) is given by \((x',y')=(k\cdot x,k\cdot y)\). Here \(k = 3\).

Step2: Identify coordinates of \(\triangle KLM\)

Let's assume the coordinates of the vertices of \(\triangle KLM\) are \(K(x_1,y_1)\), \(L(x_2,y_2)\), and \(M(x_3,y_3)\). From the graph, if \(K(- 4,0)\), \(L(-2,3)\), and \(M(2,-2)\).

Step3: Calculate new coordinates

For point \(K\):
\(x_1=-4,y_1 = 0\), \(x_1'=3\times(-4)=-12\), \(y_1'=3\times0 = 0\), so \(K'(-12,0)\).
For point \(L\):
\(x_2=-2,y_2 = 3\), \(x_2'=3\times(-2)=-6\), \(y_2'=3\times3 = 9\), so \(L'(-6,9)\).
For point \(M\):
\(x_3=2,y_3=-2\), \(x_3'=3\times2 = 6\), \(y_3'=3\times(-2)=-6\), so \(M'(6,-6)\).

Step4: Plot the new triangle

Plot the points \(K'(-12,0)\), \(L'(-6,9)\), and \(M'(6,-6)\) on the coordinate - plane and connect them to form the dilated triangle \(\triangle K'L'M'\).

Answer:

Plot the points \(K'(-12,0)\), \(L'(-6,9)\), and \(M'(6,-6)\) and connect them to get the dilated image of \(\triangle KLM\).