Question

Draw the image of ∆ABC under the dilation with scale factor 3 and center of dilation (-5, -4).

Answer 1

The image of Triangle ABC have coordinates as

A'(-2,5)

B'(-2,-1)

C'(7,-1)

Step-by-step explanation:

The figure show that Points A(-4,-1),B(-4,-3) and C(-1,-3) forms the Triangle ABC

It is asked to scaled the triangle with scale factor of 3 and centered at P(-5,-4)

For point A(-4,-1) :

Distance of A(-4,-1) from center P(-5,-4) in x-direction is 1 units and y-direction is 3 units

After scale by factor of 3,

Distance of A(-4,-1) from center P(-5,-4) is also multiply by 3

New distance in x-direction is 3 units and 9 units in y-direction from center P(-5,-4)

Therefore, New location A' is ((-5)+3,(-4)+9)=(-2,5)

For point B(-4,-3)

Distance of B(-4,-3) from center P(-5,-4) in x-direction is 1 units and y-direction is 1 units

After scale by factor of 3,

Distance of B(-4,-3) from center P(-5,-4) is also multiply by 3

New distance in x-direction is 3 units and 3 units in y-direction from center P(-5,-4)

Therefore, New location B' is ((-5)+3,(-4)+3)=(-2,-1)

For point C(-1,-3)

Distance of C(-1,-3) from center P(-5,-4) in x-direction is 4 units and y-direction is 1 units

After scale by factor of 1,

Distance of C(-1,-3) from center P(-5,-4) is also multiply by 3

New distance in x-direction is 12 units and 3 units in y-direction from center P(-5,-4)

Therefore, New location C' is ((-5)+12,(-4)+3)=(7,-1)

Therefore, The image of Triangle ABC have coordinates as

A'(-2,5)

B'(-2,-1)

C'(7,-1)