The co-ordinates of the image after translation are R"(2,1),S"(-1,7) and T"(2,7).
A translation is a geometric change in Euclidean geometry that involves moving each point in a figure, shape, or space by the same amount in one direction. A translation can also be thought of as moving the origin of the coordinate system or as adding a constant vector to each point.
When a point is rotated 90° counter clockwise, the co-ordinates of the point say A(x ,y) changes to A"(y,-x).
The given co-ordinates are: R(-7, - 5), S(-1,- 2), and T(-1.- 5 ).
So when this co-ordinates are translated by rotating 90° counterclockwise.
R(-7, -5) →R'(5,-7)
S(-1,- 2) →S'(2,-1)
T(-1.- 5) →T'(5,-1)
Now the figure is translated 3 units left and 8 units up the new co-ordinates is given by (x-3,y+8).
So when this co-ordinates are translated the new co-ordinates are:
R'(5,-7)→R"(2,1)
S'(2,-1)→S"(-1,7)
T'(5,-1)→T"(2,7)
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