Answer:
(-2,4), (0,4), (-4,-2) and (2,-2)
Step-by-step explanation:
Given
[tex]A = (-5,9)[/tex]
[tex]B = (-2,9)[/tex]
[tex]C = (-8,0)[/tex]
[tex]D = (1,0)[/tex]
[tex]Translation: 2\ units\ right\ \& \ 3\ units\ down[/tex]
[tex]Dilation: \frac{2}{3}[/tex]
Required
Determine the vertices of the image RSTU
When a coordinate (x,y) is translates b units right, the new coordinate is: (x + b, y)
So, translation 2 units right gives:
[tex]A = (-5,9)[/tex] ---> [tex]A' = (-5 + 2,9) = (-3,9)[/tex]
[tex]B = (-2,9)[/tex] ---> [tex]B' = (-2 + 2,9) = (0,9)[/tex]
[tex]C = (-8,0)[/tex] ---> [tex]C' = (-8 + 2,0) = (-6,0)[/tex]
[tex]D = (1,0)[/tex] --- > [tex]D' = (1 + 2,0) = (3,0)[/tex]
When a coordinate (x,y) is translates b units down, the new coordinate is: (x, y-b)
So, translation 3 units down gives:
[tex]A' = (-3,9)[/tex] ---> [tex]A" =(-3,9-3) =(-3,6)[/tex]
[tex]B' = (0,9)[/tex] --> [tex]B" =(0,9-3) =(0,6)[/tex]
[tex]C' = (-6,0)[/tex] --> [tex]C" =(-6,0-3) = (-6,-3)[/tex]
[tex]D' = (3,0)[/tex]--> [tex]D"=(3,0-3) = (3,-3)[/tex]
Lastly, dilation of 2/3 gives:
[tex]New = Old * \frac{2}{3}[/tex]
[tex]R = (-3,6) * \frac{2}{3} = (-2,4)[/tex]
[tex]S = (0,6) * \frac{2}{3} = (0,4)[/tex]
[tex]T = (-6,-3) * \frac{2}{3} = (-4,-2)[/tex]
[tex]U = (3,-3) * \frac{2}{3} = (2,-2)[/tex]
Hence, the coordinates of RSTU are: (-2,4), (0,4), (-4,-2) and (2,-2)
