Notes: Rotations on the coordinate plane
Rules for rotations: The following rules can be used to rotate a point 90°, 180°, or 270° counterclockwise about the
origin in the coordinate plane.
Angle of
Procedure in English
Visual
Procedure in Math
rotation
90°
Multiply the y-coordinate
by -1, then interchange the
x- and y-coordinates.
180°
Multiply the x- and ycoordinates by -1.
270°
Multiply the x-coordinate
by -1 then interchange the
x- and y-coordinates
What about clockwise rotations?
90° clockwise
(𝑥, 𝑦) → (−𝑦, 𝑥)
(𝑥, 𝑦) → (−𝑥, −𝑦)
(𝑥, 𝑦) → (𝑦, −𝑥)
180° clockwise
270° clockwise
Graph each figure and its image after the specified rotation about the origin.
Example 1) trapezoid FGHI has vertices F(7, 7), G(9, 2),
Example 2) △LMN has vertices L(–1, –1), M(0, –4), and
H(3, 2), and I(5, 7); 90° counterclockwise
N(–6, –2); 90° clockwise
Example 3) △ABC has vertices A(–3, 5), B(0, 2), and C(–
5, 1); 180°
Example 4) parallelogram PQRS has vertices P(4, 7),
Q(6, 6), R(3, –2), and S(1, –1); 270° clockwise
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Rotations on the Coordinate Plane Practice
Graph each figure and its image after the specified rotation about the origin.
1) △STU has vertices S(2, –1), T(5, 1) and U(3, 3); 90°
2) △DEF has vertices D(–4, 3), E(1, 2), and F(–3, –3);
clockwise
180°
3) quadrilateral WXYZ has vertices W(–1, 8), X(0, 4),
Y(–2, 1) and Z(–4, 3); 270° counterclockwise
4) trapezoid ABCD has vertices A(9, 0), B(6, –7), C(3, –7)
and D(0, 0); 270° clockwise
TESSELLATIONS A tessellation is when a single shape is
a)
repeated to tile a plane with no gaps or overlaps. Below is
an example of triangle △RST rotated around the point R.
This forms a tessellation.
b)