IXL - Transformation matrices: write the vertex matrix (Precalculus practice)

Use a transformation matrix to find the image of

(

–

)

after a translation of 9 units right and 8 units down.

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Learn with an example

question

Use a transformation matrix to find the image of

(

)

after a rotation of 270° counterclockwise around the origin.

key idea

A point

(

)

can be written as a

matrix. Write the

-coordinate

in the first row and the

-coordinate

in the second row.

A vertex matrix is useful because you can multiply it by another matrix to perform certain types of transformations on the shape. The matrix for the transformation should be multiplied on the left of the vertex matrix.

Transformation name	Matrix
Reflection across the x -axis	1 0 0 – 1
Reflection across the y -axis	– 1 0 0 1
Reflection across x = y	0 1 1 0
Reflection across – x = y	0 – 1 – 1 0
Rotation of 90° counterclockwise around the origin	0 – 1 1 0
Rotation of 180° counterclockwise around the origin	– 1 0 0 – 1
Rotation of 270° counterclockwise around the origin	0 1 – 1 0

solution

Write

(

)

as a

matrix.

To find the image of the point, first find the rotation matrix. A rotation of 270° counterclockwise around the origin is represented by:

–

Now multiply the matrix representing the point by the rotation matrix on the left.

–

Write the image as a coordinate pair. The image of

(

)

after a rotation of 270° counterclockwise around the origin is

(

–

)

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Teacher tools

Work it out

Not feeling ready yet? These can help:

Q.16Identify transformation matrices

Q.6Multiply two matrices

Q.3Add and subtract matrices

Q.4Multiply a matrix by a scalar

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