The coordinates of the image of triangle P'Q'R' after a rotation, translation, and reflection are (-4, -1), (-3, -3), and (-2, 0).
What is a rotation?
In Mathematics, rotating a point 90° about the origin in a clockwise or counterclockwise direction would produce a point that has these coordinates (y, -x).
By applying a rotation of 90° clockwise to triangle PQR, the coordinate of the image of triangle P'Q'R' is given by:
(x, y) → (y, -x)
Points at P = (-4, 4) → Points at P' = (4, -(-4)) = (4, 4)
Points at Q = (-2, 3) → Points at Q' = (3, -(-2)) = (3, 2).
Points at R = (-5, 2) → Points at R' = (2, -(-5)) = (2, 5).
Next, we would translate the coordinates of the image of triangle P'Q'R' 5 units down:
Points at P' = (4, 4) = (4, (4 - 5)) = (4, -1)
Points at Q' = (3, 2) = (3, (2 - 5)) = (3, -3)
Points at R' = (2, 5) = (2, (5 - 5) = (2, 0).
Lastly, we would reflect the coordinates of the image of triangle P'Q'R' across the y-axis:
(x, y) → (-x, y)
Points at P' = (4, -1) = (-4, -1)
Points at Q' = (3, -3) = (-3, -3)
Points at R' = (2, 0) = (-2, 0).
Read more on rotation here: brainly.com/question/28515054
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