Answer:
- M"(-5, -7)
- N"(-5, -3)
- O"(0, -3)
Explanation:
Each of the transformations can be written in terms of what they do to the coordinates:
(x, y) ⇒ (-y, x) . . . . . . rotation 90° CCW
(x, y) ⇒ (x -7, y-8) . . . . translation 7 left and 8 down
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Together, these transformations result in the composite transformation ...
(x, y) ⇒ (-y -7, x -8)
The end values of the original points are then ...
M(1, -2) ⇒ M"(-(-2) -7, 1 -8) = M"(-5, -7)
N(5, -2) ⇒ N"(-(-2) -7, 5 -8) = N"(-5, -3)
O(5, -7) ⇒ O"(-(-7)-7, 5 -8) = O"(0, -3)
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Additional comment
You can get an idea of what the 90° rotation looks like by printing the figure and turning it 1/4 turn counterclockwise. The points will have the same relative locations with respect to the axes. Effectively, you are relabeling the x-axis to y, and the -y axis to x. (That is what the 90° CCW transformation formula is telling you.)
Alternatively, you can turn your head sideways when you look at the computer screen.
In the attachment, the black arrow represents the translation vector, 7 left and 8 down.