The image of the point (1, -2) after a rotation of 180° about the origin is

Solution:

A rotation is a transformationin 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 180 degrees clockwise is the same as rotating a figure 90 degrees counterclockwise.

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

So, the image of the point (1, -2) after a rotation of 180° about the origin is

(1, -2) = (-1, -(-2))

= (-1, 2)

Therefore, the image of the point after rotation is (-1, 2).

Example:

The image of the point (-1, -3) after a rotation of 180° about the origin is

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

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

So, the image of the point (-1, -3) after a rotation of 180° about the origin is

(-1, -3) = (-(-1), -(-3))

= (1, 3)

Therefore, the image of the point after rotation is (1, 3).

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The image of the point (1, -2) after a rotation of 180° about the origin is

Summary:

The image of the point (1, -2) after a rotation of 180° about the origin is (-1, 2).