Translations and Reflections

Front

What is a translation in geometry?

Back

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

Tags

CCSS.8.G.A.3

CCSS.HSG.CO.A.5

Front

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

Back

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

Tags

CCSS.8.G.A.3

CCSS.HSG.CO.A.5

Front

What is the result of translating the point (2, 3) by (3, -2)?

Back

The new point after translation is (2+3, 3-2) = (5, 1).

Tags

CCSS.8.G.A.3

CCSS.HSG.CO.A.5

Front

What does it mean to reflect a shape across the y-axis?

Back

Reflecting a shape across the y-axis means that each point (x, y) of the shape is transformed to (-x, y).

Tags

CCSS.8.G.A.3

CCSS.HSG.CO.A.5

Front

What is the result of reflecting the point (4, 5) across the y-axis?

Back

The new point after reflection is (-4, 5).

Tags

CCSS.8.G.A.3

CCSS.HSG.CO.A.5

Front

What does it mean to reflect a shape across the x-axis?

Back

Reflecting a shape across the x-axis means that each point (x, y) of the shape is transformed to (x, -y).

Tags

CCSS.8.G.A.3

CCSS.HSG.CO.A.5

Front

What is the result of reflecting the point (3, -2) across the x-axis?

Back

The new point after reflection is (3, 2).

Tags

CCSS.8.G.A.3

CCSS.HSG.CO.A.5

Front

If a shape is translated 5 units down and 4 units to the right, what is the translation vector?

Back

The translation vector is (4, -5).

Tags

CCSS.8.G.A.3

CCSS.HSG.CO.A.5

Front

How do you determine the new position of a shape after a translation?

Back

You apply the translation vector to each vertex of the shape by adding the vector's components to the coordinates of the vertices.

Tags

CCSS.8.G.A.3

CCSS.HSG.CO.A.5

Front

What is the effect of translating a shape 3 units left and 3 units down?

Back

The shape moves to the left and downward, changing each point (x, y) to (x-3, y-3).

Tags

CCSS.8.G.A.3

CCSS.HSG.CO.A.5