IXL - Identify transformation matrices (Precalculus practice)

is a vertex matrix, which transformation does

–

represent?

reflection

rotation

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Learn with an example

question

is a vertex matrix, which transformation does

represent?

reflection

rotation

key idea

Each column of a vertex matrix is a coordinate pair of a vertex. For example, the vertex matrix of

△

with vertices

(

)

(

–

)

and

(

)

is:

–

Write the

-coordinates

in the first row and the

-coordinates

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

The product

represents a reflection across

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Teacher tools

Work it out

Not feeling ready yet? These can help:

H.9Rotations: find the coordinates

H.6Reflections: find the coordinates

I.2Dilations: find the coordinates

H.3Translations: find the coordinates

Q.6Multiply two matrices

Q.3Add and subtract matrices

Q.4Multiply a matrix by a scalar

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