Transformations and Dilations

Front

What is a transformation in geometry?

Back

A transformation is a mathematical operation that moves or changes a shape in some way, such as translation, rotation, reflection, or dilation.

Tags

CCSS.8.G.A.3

CCSS.HSG.CO.A.5

Front

Define translation in geometry.

Back

Translation is a type of transformation that slides a shape from one position to another without turning it. It is defined by a vector that indicates the direction and distance of the slide.

Tags

CCSS.8.G.A.3

CCSS.HSG.CO.A.5

Front

What is a rotation in geometry?

Back

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

Tags

CCSS.8.G.A.3

CCSS.HSG.CO.A.5

Front

What is reflection in geometry?

Back

Reflection is a transformation that flips a shape over a line, creating a mirror image of the original shape.

Tags

CCSS.8.G.A.3

CCSS.HSG.CO.A.5

Front

Define dilation in geometry.

Back

Dilation is a transformation that changes the size of a shape but not its shape. It is defined by a center of dilation and a scale factor.

Tags

CCSS.8.G.A.3

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. A scale factor greater than 1 enlarges the shape, while a scale factor between 0 and 1 reduces it.

Tags

CCSS.8.G.A.3

Front

How do you perform a translation of a point (x, y) by (a, b)?

Back

To translate the point (x, y) by (a, b), you add a to the x-coordinate and b to the y-coordinate, resulting in the new point (x+a, y+b).

Tags

CCSS.8.G.A.3

CCSS.HSG.CO.A.5

Front

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

Back

When a point (x, y) is reflected over the x-axis, its new coordinates become (x, -y).

Tags

CCSS.8.G.A.3

CCSS.HSG.CO.A.5

Front

How do you rotate a point (x, y) 90 degrees counterclockwise about the origin?

Back

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

Tags

CCSS.8.G.A.3

CCSS.HSG.CO.A.5

Front

What is the result of dilating a point (x, y) with a scale factor k?

Back

The new coordinates of the point (x, y) after dilation with a scale factor k are (kx, ky).

Tags

CCSS.8.G.A.3