Rotations and Dilations in a coordinate plane

Front

What is a rotation in a coordinate plane?

Back

A rotation is a transformation that turns a figure around a fixed point, called the center of rotation, by a specified angle in a specified direction.

Front

What is the rule for rotating a point (x, y) 90 degrees counterclockwise about the origin?

Back

The rule is (-y, x).

Front

What is the rule for rotating a point (x, y) 180 degrees about the origin?

Back

The rule is (-x, -y).

Front

What is the rule for rotating a point (x, y) 270 degrees counterclockwise about the origin?

Back

The rule is (y, -x).

Front

What is dilation in a coordinate plane?

Back

Dilation is a transformation that changes the size of a figure but not its shape, using a scale factor.

Front

If a triangle has vertices at A(2,3), B(-5,-1), and C(0,5), what are the coordinates of the triangle after a dilation with a scale factor of 2?

Back

A'(4,6), B'(-10,-2), C'(0,10).

Front

How do you determine the scale factor in a dilation?

Back

The scale factor is determined by comparing the lengths of corresponding sides of the original figure and the dilated figure.

Front

What is the effect of a scale factor less than 1 in dilation?

Back

A scale factor less than 1 reduces the size of the figure.

Front

What is the effect of a scale factor greater than 1 in dilation?

Back

A scale factor greater than 1 enlarges the size of the figure.

Front

If triangle C is rotated 180° clockwise, what is the new position of point C(3,4)?

Back

The new position is C'(-3,-4).