Answer:
[tex]B' = (-3, -15)[/tex]
Step-by-step explanation:
Given
[tex]A = (-3,-1)[/tex]
[tex]A' = (-9,-3)[/tex]
[tex]B = (-1,-5)[/tex]
Required
Determine the coordinates of B'
Since A' is the image of A; we need to first calculate the scale factor using
[tex]A' = A * Scale\ factor[/tex]
Make Scale Factor the subject
[tex]Scale\ Factor = \frac{A'}{A}[/tex]
Substitute values for A' and A
[tex]Scale\ Factor = \frac{(-9,-3)}{(-3, -1)}[/tex]
Factorize the numerator
[tex]Scale\ Factor = \frac{3 * (-3,-1)}{(-3, -1)}[/tex]
[tex]Scale\ Factor = \frac{3 * 1}{1}[/tex]
[tex]Scale\ Factor = 3[/tex]
The coordinates of B' is then calculated as follows:
[tex]B' = B * Scale\ Factor[/tex]
Substitute values for B and Scale Factor
[tex]B' = (-1,-5) * 3[/tex]
[tex]B' = (-3, -15)[/tex]
