Question

name:
assessment (4.4 to 4.6): sim

1. graph (\triangle abc) with vertices (a(-2,1)), (b(-2,-1)),

and (c(2,-2)) and its image after a dilation with a
scale factor of 2.
(show work-1 point)

Explanation:

Step1: Recall the dilation formula

For a dilation with scale factor \(k\) centered at the origin \((0,0)\), if a point \(P(x,y)\) is dilated, the image \(P'(x',y')\) is given by \(x' = kx\) and \(y'=ky\). Here \(k = 2\).

Step2: Find the coordinates of the dilated points

• For point \(A(-2,1)\):

\(x'=2\times(-2)=-4\), \(y'=2\times1 = 2\). So \(A'(-4,2)\)

• For point \(B(-2,-1)\):

\(x'=2\times(-2)=-4\), \(y'=2\times(-1)=-2\). So \(B'(-4,-2)\)

• For point \(C(2,-2)\):

\(x'=2\times2 = 4\), \(y'=2\times(-2)=-4\). So \(C'(4,-4)\)

Answer:

The coordinates of the dilated triangle \(A'B'C'\) are \(A'(-4,2)\), \(B'(-4,-2)\) and \(C'(4,-4)\)