Transformations: Translations, Reflections, Rotations, and Dilations

Front

What is a translation in geometry?

Back

A translation is a transformation that moves every point of a shape the same distance in a specified direction.

Front

How do you reflect a point over the y-axis?

Back

To reflect a point (x, y) over the y-axis, the new coordinates become (-x, y).

Front

What is the result of reflecting the point (3, 4) over the x-axis?

Back

The result is (3, -4).

Front

Define dilation in geometry.

Back

Dilation is a transformation that alters the size of a shape but keeps its proportions the same, defined by a center of dilation and a scale factor.

Front

What happens to the coordinates of a point (x, y) when it is reflected over the line y = x?

Back

The coordinates become (y, x).

Front

What is the scale factor in dilation?

Back

The scale factor is a number that describes how much a shape is enlarged or reduced during a dilation.

Front

How do you rotate a point 90 degrees counterclockwise about the origin?

Back

To rotate a point (x, y) 90 degrees counterclockwise, the new coordinates become (-y, x).

Front

What is the effect of a 180-degree rotation about the origin on the point (a, b)?

Back

The new coordinates become (-a, -b).

Front

How do you perform a reflection over the line y = -x?

Back

To reflect a point (x, y) over the line y = -x, the new coordinates become (-y, -x).

Front

What is the center of dilation?

Back

The center of dilation is the fixed point in a plane about which all points are expanded or contracted.