EXAMPLE 5 Use matrix multiplication to reflect a polygon

SOLUTION

The vertices of DEF are D(1, 2), E(3, 3), and F(4, 0). Find the reflection of DEF in the y-axis using matrix multiplication. Graph DEF and its image.

STEP 1

Multiply the polygon matrix by the matrix for a reflection in the y-axis.

–1 0

0 1

Reflection matrix

+1 3 4

2 3 0

Polygon matrix

D E F

EXAMPLE 5 Use matrix multiplication to reflect a polygon

–1(1) + 0(2) –1(3) + 0(3) –1(4) + 0(0)=

0(1) + 1(2) 0(3) + 1(3) 0(4) + 1(0)

–1 –3 –4

2 3 0=

Image matrix

D′ E′ F′

EXAMPLE 5 Use matrix multiplication to reflect a polygon

STEP 2

Graph DEF and D′E′F′.

The vertices of LMN are L(–3, 3), M(1, 2), and N(–2, 1).

reflection using matrix multiplication.Find the described

GUIDED PRACTICE for Example 5

SOLUTION

STEP 1

Multiply the polygon matrix by the matrix for a reflection in the y-axis.

7. Reflect LMN in the x-axis.

GUIDED PRACTICE for Example 5

1(–2) + 0(1) =

0(–3 ) + –1(3) 0(1) + –1(2)

1(–3 ) + 0(3) 1(1) + 0(2)

0(–2) + –1(1)

–3 –2 –1

L′ M′ N′

–3 1 –2

Image Matrix

=

1 0

0 –1 3 2 1

L M N

Reflection matrix

Polygon matrix

–3 1 –2

The vertices of LMN are L(–3, 3), M(1, 2), and N(–2, 1).

reflection using matrix

multiplication.

Find the described

GUIDED PRACTICE for Example 5

SOLUTION

STEP 1

Multiply the polygon matrix by the matrix for a reflection in the x-axis.

8. Reflect LMN in the y-axis.

GUIDED PRACTICE for Example 5

–1 0

0 1 3 2 1

L M N

Reflection matrix

Polygon matrix

–1(–2) + 0(1) =

0(–3 ) + 1(3) 0(1) + 1(2)

–1(–3 ) + 0(3) –1 (1) + 0(2)

0(–2) + 1(1)

3 2 1

L′ M′ N′

3 –1 2

Image Matrix

=

–3 1 –2