When a triangle is dilated, the size of the triangle changes.
The image of [tex]\triangle A'B'C'[/tex] are:
[tex]A' = (7,12)[/tex]
[tex]B' = (13,8)[/tex]
[tex]C' =(5,0)[/tex]
We have:
[tex]A = (9,13)[/tex]
[tex]B = (12,11)[/tex]
[tex]C = (8,7)[/tex]
[tex]k = 2[/tex]
Start by multiplying the scale factor by the coordinates of [tex]\triangle ABC[/tex]
[tex]A = (9,13) \times 2[/tex]
[tex]A = (18,26)[/tex]
[tex]B = (12,11) \times 2[/tex]
[tex]B = (24,22)[/tex]
[tex]C =(8,7) \times 2[/tex]
[tex]C =(16,14)[/tex]
Subtract the center of dilation from the above coordinates
[tex]A' = (18,26) - (11,14)[/tex]
[tex]A' = (18-11,26-14)[/tex]
[tex]A' = (7,12)[/tex]
[tex]B' = (24,22) - (11,14)[/tex]
[tex]B' = (24-11,22-14)[/tex]
[tex]B' = (13,8)[/tex]
[tex]C' =(16,14) - (11,14)[/tex]
[tex]C' =(16 - 11,14 - 14)[/tex]
[tex]C' =(5,0)[/tex]
Hence, the image of [tex]\triangle A'B'C'[/tex] are:
[tex]A' = (7,12)[/tex]
[tex]B' = (13,8)[/tex]
[tex]C' =(5,0)[/tex]
Read more about dilations at:
https://brainly.com/question/13176891
