Question

consider △abc and its dilation, △abc. the center of the dilation is at the origin. write the coordinates of each vertex of △abc.
△abc
a (-2, -2)
b (2, -2)
c (4, -4)
△abc
a ( , )
b ( , )
c ( , )
the scale factor for the dilation of △abc is

is a(n)

when an original figure is dilated, if the scale factor is 1, then the original figure and its dilation are congruent. otherwise, if the scale factor is not 0, the original figure and its dilation are similar.

figures

△abc and △abc are

Explanation:

Step1: Recall the formula for dilation

When a point \((x,y)\) is dilated with a scale factor \(k\) and center at the origin \((0,0)\), the new point \((x',y')\) is given by \((x',y')=(kx,ky)\).

Step2: Determine the scale factor

Looking at the figure (or using the property of similar figures in dilation), assume the scale factor \(k = 2\) (by comparing the side - lengths of \(\triangle ABC\) and \(\triangle A'B'C'\)).

Step3: Calculate the coordinates of \(A'\)

For point \(A(-2,-2)\), using the dilation formula \((x',y')=(kx,ky)\) with \(k = 2\), we have \(x'=2\times(-2)=- 4\) and \(y'=2\times(-2)=-4\). So \(A'(-4,-4)\)

Step4: Calculate the coordinates of \(B'\)

For point \(B(2,-2)\), using the dilation formula \((x',y')=(kx,ky)\) with \(k = 2\), we have \(x'=2\times2 = 4\) and \(y'=2\times(-2)=-4\). So \(B'(4,-4)\)

Step5: Calculate the coordinates of \(C'\)

For point \(C(4,-4)\), using the dilation formula \((x',y')=(kx,ky)\) with \(k = 2\), we have \(x'=2\times4 = 8\) and \(y'=2\times(-4)=-8\). So \(C'(8,-8)\)

Answer:

\(A'(-4,-4)\), \(B'(4,-4)\), \(C'(8,-8)\)