Question

name:
assessment (4.4 to 4.6): similarity

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)

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Explanation:

Step1: Recall the dilation formula

For a dilation with scale factor \(k\) centered at the origin, if a point \(P(x,y)\) is dilated, its 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 \(A(-2,1)\):

Using the formula \(x'=k x\) and \(y' = k y\), with \(k = 2\), \(x'=2\times(-2)=-4\) and \(y'=2\times1 = 2\). So \(A'(-4,2)\).

• For point \(B(-2,-1)\):

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

• For point \(C(2,-2)\):

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

Step3: Graph the original and dilated triangles

Plot the original points \(A(-2,1)\), \(B(-2,-1)\), \(C(2,-2)\) and the dilated points \(A'(-4,2)\), \(B'(-4,-2)\), \(C'(4,-4)\) on the coordinate - plane. Connect the points \(A - B - C\) for \(\triangle ABC\) and \(A' - B' - C'\) for the dilated triangle.

Answer:

The coordinates of the dilated triangle \(\triangle A'B'C'\) are \(A'(-4,2)\), \(B'(-4,-2)\), \(C'(4,-4)\). Graph \(\triangle ABC\) with vertices \(A(-2,1)\), \(B(-2,-1)\), \(C(2,-2)\) and \(\triangle A'B'C'\) with vertices \(A'(-4,2)\), \(B'(-4,-2)\), \(C'(4,-4)\) on the given coordinate - plane.