The quadrilateral A'R'M'Y' is formed by rotating 90° the quadrilateral ARMY, whose vertices are A'(x, y) = (- 3, 3), R'(x, y) = (- 7, 5), M'(x, y) = (- 5, 7) and Y'(x, y) = (- 1, 5).
How to obtain a resulting quadrilateral by rotation about the origin
This problem requires us to find the coordinates about the origin by applying a rigid transformation known as a rotation. Rigid transformations are transformations applied on geometric loci such that Euclidean distances are conserved.
The rotation about the origin is described by the following expressions:
x' = x · cos θ - y · sin θ (1)
y' = x · sin θ + y · cos θ (2)
If we know that A(x, y) = (3, 3), R(x, y) = (5, 7), M(x, y) = (7, 5), Y(x, y) = (5, 1) and θ = 90°, then the points of the image are:
A'(x, y) = (3 · cos 90° - 3 · sin 90°, 3 · sin 90° + 3 · cos 90°)
A'(x, y) = (- 3, 3)
R'(x, y) = (5 · cos 90° - 7 · sin 90°, 5 · sin 90° + 7 · cos 90°)
R'(x, y) = (- 7, 5)
M'(x, y) = (7 · cos 90° - 5 · sin 90°, 7 · sin 90° + 5 · cos 90°)
M'(x, y) = (- 5, 7)
Y'(x, y) = (5 · cos 90° - 1 · sin 90°, 5 · sin 90° + 1 · cos 90°)
Y'(x, y) = (- 1, 5)
The picture with the two quadrilaterals is attached below.
To learn more on rotations: https://brainly.com/question/1571997
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