Graph Rotations
14-7
A rotation is a transformation that turns a figure about a point in either
a clockwise or in a counterclockwise direction. The point around which
a figure rotates is called the center of rotation.
To describe a rotation, tell whether the turn is clockwise or counterclockwise
and the number of degrees through which the figure is turned.
A rotation of 90°is a quarter turn.
A rotation of 180°is a half turn.
A rotation of270°is athree-quarter turn.
You can draw a rotation of a point P(x, y) counterclockwise
about the origin on a coordinate plane.
The rotation image point P′(x, y) is:
(y, x)if the rotation is 90°.
P(3, 1) P′(1, 3)
A 90°-rotation changes the sign of
the y-coordinate and then reverses
the order of the coordinates.
A 180°-rotation changes the signs
of both x- and y-coordinates.
(x, y)if the rotation is 180°.
P(3, 1) P′(3, 1)
A 270°-rotation changes the sign of
the x-coordinate and then reverses
the order of the coordinates.
(y, x)if the rotation is 270°.
P(3, 1) P′(1, 3)
You can rotate OAB90°
counterclockwise about the origin.
O(0, 0), A(3, 0), B(3, 4)
O′(0, 0), A′(0, 3), B′(4, 3)
Rotate each
vertex 90°
counterclockwise.
Label the new
vertices O′, A′,
and B′.
Connect the points.
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