Question

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

Explanation:

Step1: Identify coordinates of vertices

Let \(K(- 3,0)\), \(L(-3,3)\), \(M(2,-2)\).

Step2: Apply dilation formula

For a dilation centered at the origin with scale - factor \(k = 3\), the formula is \((x,y)\to(kx,ky)\).
For point \(K\): \((-3,0)\to(3\times(-3),3\times0)=(-9,0)\)
For point \(L\): \((-3,3)\to(3\times(-3),3\times3)=(-9,9)\)
For point \(M\): \((2,-2)\to(3\times2,3\times(-2))=(6,-6)\)

Step3: Graph new triangle

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

Answer:

Graph the triangle with vertices \(K'(-9,0)\), \(L'(-9,9)\), \(M'(6,-6)\) on the given coordinate - plane.