What is the algebraic rule for a figure that is rotated 270° clockwise about the origin?

Solution:

A rotation is a transformation in a plane that turns every point of a preimage through a specified angle and direction about a fixed point. The fixed point is called the center of rotation.

The amount of rotation is called the angle of rotation and it is measured in degrees.

Rotating a figure 270 degrees clockwise is the same as rotating a figure 90 degrees counterclockwise.

Now, it would be (x, y) = (-y, x)

Example:

What will be the coordinate of a point having coordinates (3,-6) after rotations as 90° anti-clockwise and 270° clockwise?

Solution:

Given, the coordinate of a point is (3, -6)

Rotating 90° anticlockwise, (x, y) becomes (-y, x)

So, (3, -6) = (-(-6), 3)

The coordinate of a point is (6, 3)

Rotating 270° clockwise, (x, y) becomes (y, -x)

So, (3, -6) = (-6, -3)

The coordinate of a point is (-6, -3).

Therefore, the coordinate of a point (3, -6) after rotating 90° anticlockwise and 270° clockwise is (-6, -3).

Therefore, the algebraic rule for a figure that is rotated 270° clockwise about the origin is (y, -x)

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What is the algebraic rule for a figure that is rotated 270° clockwise about the origin?

Summary:

The algebraic rule for a figure that is rotated 270° clockwise about the origin is (y, -x).