Question

in the coordinate plane, you can extend dilations to include scale factors that are negative numbers. use \\( \triangle pqr \\) with vertices \\( p(1,3) \\), \\( q(3,3) \\), and \\( r(3,1) \\).
graph \\( \triangle pqr \\) and its image for a dilation centered at \\( (0,0) \\) with scale factor \\( -3 \\).
choose the correct graph below.
oa.
ob.
oc.
od.

Explanation:

Step1: Recall the dilation formula

If we have a dilation centered at the origin \((0,0)\) with a scale factor \(k\), and a point \((x,y)\) in the original figure, the image of the point after dilation is \((kx,ky)\). Here \(k =- 3\), and the vertices of \(\triangle PQR\) are \(P(1,3)\), \(Q(3,3)\), and \(R(3,1)\).

Step2: Calculate the image of each vertex

• For point \(P(1,3)\):

Using the formula \((x',y')=(kx,ky)\) with \(k =-3\), we get \(P'(-3\times1,-3\times3)=(-3,-9)\)

• For point \(Q(3,3)\):

Using the formula \((x',y')=(kx,ky)\) with \(k =-3\), we get \(Q'(-3\times3,-3\times3)=(-9,-9)\)

• For point \(R(3,1)\):

Using the formula \((x',y')=(kx,ky)\) with \(k =-3\), we get \(R'(-3\times3,-3\times1)=(-9,-3)\)

Answer:

A.