Transformations on Coordinate Plane

Front

What is a transformation in the context of the coordinate plane?

Back

A transformation is an operation that moves or changes a shape in the coordinate plane, including translations, reflections, rotations, and dilations.

Front

Define translation in the coordinate plane.

Back

Translation is a transformation that slides a figure in a straight line from one position to another without changing its shape, size, or orientation.

Front

What is reflection across the y-axis?

Back

Reflection across the y-axis is a transformation that flips a figure over the y-axis, changing the sign of the x-coordinates of the points.

Front

What is the rule for reflecting a point (x, y) across the y-axis?

Back

The rule is (x, y) -> (-x, y).

Front

Define rotation in the coordinate plane.

Back

Rotation is a transformation that turns a figure around a fixed point, known as the center of rotation, by a certain angle.

Front

What is the rule for a 90° counterclockwise rotation around the origin?

Back

The rule is (x, y) -> (-y, x).

Front

What is the effect of translating a point (x, y) by (x + 2, y - 1)?

Back

The new point will be (x + 2, y - 1), meaning it moves 2 units to the right and 1 unit down.

Front

How do you identify a translation from one set of coordinates to another?

Back

By comparing the changes in the x and y coordinates of the original and new points.

Front

What happens to the coordinates of a point when it is reflected across the x-axis?

Back

The y-coordinate changes sign, so (x, y) becomes (x, -y).

Front

If a triangle has vertices at (4, 2), (5, 1), and (3, 7), what are the new coordinates after reflecting across the y-axis?

Back

The new coordinates will be (-4, 2), (-5, 1), and (-3, 7).