Question

graph the polygon with the given vertices and its image after a dilation with scale factor k. l(0,0), m(-4,1), n(-3,-6); k=-3

Explanation:

Step1: Apply dilation formula

The formula for dilation is \((x,y)\to(kx,ky)\). Given \(k = - 3\), for point \(L(0,0)\):

$$
LATEXBLOCK0
$$

For point \(M(-4,1)\):

$$
LATEXBLOCK1
$$

For point \(N(-3,-6)\):

$$
LATEXBLOCK2
$$

Step2: Plot the original and dilated points

• Original polygon: Plot \(L(0,0)\), \(M(-4,1)\), \(N(-3,-6)\) on the coordinate - grid.
• Dilated polygon: Plot \(L'(0,0)\), \(M'(12,-3)\), \(N'(9,18)\) on the coordinate - grid. Then connect the points of the original polygon (\(L - M - N - L\)) and the dilated polygon (\(L' - M' - N' - L'\)).

Answer:

• Original polygon vertices: \(L(0,0)\), \(M(-4,1)\), \(N(-3,-6)\)
• Dilated polygon vertices (using the dilation formula \((x,y)\to(-3x,-3y)\)): \(L'(0,0)\), \(M'(12, - 3)\), \(N'(9,18)\). Plot these points on the given coordinate - grid and connect them as described in Step 2.