The image by rotation of the triangle ABC with vertices A(x, y) = (8, - 9), B(x, y) = (5, - 4), C(x, y) = (7, - 1) is represented by vertices A'(x, y) = (- 9, - 8), B'(x, y) = (- 4, - 5) and C'(x, y) = (- 1, - 7). The transformation rule is R'(x, y) = (x · cos θ - y · sin θ, x · sin θ + y · cos θ).
How to find the transformation rule and image of a given figure
In this problem we have the case of triangle set on a Cartesian plane and that must be rotated 90° clockwise, the image can be found by using the following transformation rule:
R'(x, y) = (x · cos θ - y · sin θ, x · sin θ + y · cos θ)
Where:
x, y - Coordinates of the original point.
θ - Angle of rotation, in degrees.
If we know that A(x, y) = (8, - 9), B(x, y) = (5, - 4), C(x, y) = (7, - 1) and θ = - 90°, then the image of the triangle is:
A'(x, y) = (8 · cos (- 90°) - (- 9) · sin (- 90°), 8 · sin (- 90°) + (- 9) · cos (- 90°))
A'(x, y) = (- 9, - 8)
B'(x, y) = (5 · cos (- 90°) - (- 4) · sin (- 90°), 5 · sin (- 90°) + (- 4) · cos (- 90°))
B'(x, y) = (- 4, - 5)
C'(x, y) = (7 · cos (- 90°) - (- 1) · sin (- 90°), 7 · sin (- 90°) + (- 1) · cos (- 90°))
C'(x, y) = (- 1, - 7)
To learn more on transformation rules: https://brainly.com/question/21298384
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