Graph the image of this figure after a dilation with a scale factor of 3 centered at (−7, −6) .

The vertices of the dilated triangles are ( 5,6 ), ( 2,-3 ) and ( -7,3 ) and the new triangle is shown in the figure.

Step-by-step explanation:

We are given a triangle having vertices ( -3,-2 ), ( -4,-5 ) and ( -7,-3 ).

The center for the dilation is ( -7,-6 ).

Now, the formula for the new dilated point is given by,

Dilated point = [ Old point - Dilated Center ] × Scale Factor + Dilated Center.

So, we have the new points as:

A. For ( -3,-2 )

Dilated point = [ ( -3,-2 ) - ( -7,-6 )] × 3 + ( -7,-6 )

i.e. Dilated point = ( 4,4 ) × 3 + ( -7,-6 )

i.e. Dilated point = ( 12,12 ) + ( -7,-6 )

i.e. Dilated point = ( 5,6 )

B. For ( -4,-5 )

Dilated point = [ ( -4,-5 ) - ( -7,-6 )] × 3 + ( -7,-6 )

i.e. Dilated point = ( 3,1 ) × 3 + ( -7,-6 )

i.e. Dilated point = ( 9,3 ) + ( -7,-6 )

i.e. Dilated point = ( 2,-3 )

C. For ( -7,-3 )

Dilated point = [ ( -7,-3 ) - ( -7,-6 )] × 3 + ( -7,-6 )

i.e. Dilated point = ( 0,3 ) × 3 + ( -7,-6 )

i.e. Dilated point = ( 0,9 ) + ( -7,-6 )

i.e. Dilated point = ( -7,3 )

So, the vertices of the dilated triangles are ( 5,6 ), ( 2,-3 ) and ( -7,3 ) and the new triangle is shown in the figure.