Question

consider \\( \triangle p q r \\) in the coordinate plane.
a. what are the coordinates of the images of vertices \\( p, q \\), and \\( r \\) under a dilation centered at the origin with scale factor 1.5?
coordinates of \\( p \\)
coordinates of \\( q \\)
coordinates of \\( r \\)

Explanation:

Step1: Find coordinates of \(P\), \(Q\), \(R\)

From the graph, \(P(-6,2)\), \(Q(-3,4)\), \(R(-1,4)\)

Step2: Apply dilation formula

For a dilation centered at the origin \((x,y)\to(kx,ky)\) where \(k = 1.5\)
For \(P(-6,2)\):
\(P'=(1.5\times(-6),1.5\times2)=(-9,3)\)
For \(Q(-3,4)\):
\(Q'=(1.5\times(-3),1.5\times4)=(-4.5,6)\)
For \(R(-1,4)\):
\(R'=(1.5\times(-1),1.5\times4)=(-1.5,6)\)

Answer:

Coordinates of \(P'\): \((-9,3)\)
Coordinates of \(Q'\): \((-4.5,6)\)
Coordinates of \(R'\): \((-1.5,6)\)