IXL - Transformation matrices: graph the image (Precalculus practice)

Use a transformation matrix to graph the image of

(

–

)

after a translation of 3 units left and 8 units down.

Coordinate plane graph with 4 quadrants, x-axis coordinates from -10 to 10, y-axis coordinates from -10 to 10. The following data are shown. Point (-2, -1).

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Learn with an example

question

Use a transformation matrix to graph the image of

(

)

after a reflection across the

-axis.

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 reflection matrix. A reflection across the

-axis

is represented by:

–

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

–

Write the image as a coordinate pair. The image of

(

)

after a reflection across the

-axis

(

–

)

Plot the image.

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Q.17Transformation matrices: write the vertex matrix

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