Question

Graph the polygon and it’s image after dilation centered at (0,0)

Answer 1

When we dilate a figure centered at the origin by a factor k, the new coordinates will be equal to the old coordinates multiplied by the scale factor.

`(x,y)\to(kx,ky)`

The original vertices of our figure are:

`L(0,0),M(-4,1),N(-3,-6)`

Then, dilating our figure with a scale factor equal to -3, we have:

`\begin{gathered} L(0,0)\to L^(\prime)((-3)\cdot0,(-3)\cdot0)=L^(\prime)(0,0) \\ M(-4,1)\to M^(\prime)((-3)\cdot(-4),(-3)\cdot1)=M^(\prime)(12,-3) \\ N(-3,-6)\to N^(\prime)((-3)\cdot(-3),(-3)\cdot(-6))=N^(\prime)(9,18) \end{gathered}`

The coordinates of the image are

`L^(\prime)(0,0),M^(\prime)(12,-3),N^(\prime)(9,18)`