Question

write the coordinates of the vertices after a dilation with a scale factor of 2, centered at the origin.

(graph with axes, grid, and triangle with vertices p, q, r. below the graph: p(□, □), q(□, □), r(□, □))

Explanation:

Step1: Find original coordinates

From the graph, the original coordinates are \(P(-6,-3)\), \(Q(2,-3)\), \(R(-2,-2)\).

Step2: Apply dilation formula

The formula for dilation centered at the origin with scale factor \(k\) is \((x,y)\to(kx,ky)\). Here \(k = 2\).
For \(P(-6,-3)\): \((-6\times2,-3\times2)=(-12,-6)\)
For \(Q(2,-3)\): \((2\times2,-3\times2)=(4,-6)\)
For \(R(-2,-2)\): \((-2\times2,-2\times2)=(-4,-4)\)

Answer:

\(P(-12,-6)\), \(Q(4,-6)\), \(R(-4,-4)\)