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Objective

Identify figures with line symmetry and graph reflections on a coordinate plane

Vocabulary

Line symmetry

Figures that match exactly when folded in half

Vocabulary

Lines of symmetry

A line that divides a figure into two halves that are reflections of each other

Vocabulary

Reflections

A type of transformation in which a figure is flipped over a line of symmetry

Example 1 Identify Lines of Symmetry

Example 2 Identify Lines of Symmetry

Example 3 Identify Lines of Symmetry

Example 4 Reflect a Figure Over the x-axis

Example 5 Reflect a Figure Over the y-axis

Draw figure then determine whether the figure has line symmetry. If it does, draw all lines of symmetry. If it has no line symmetry, say “no symmetry”

Answer: Two lines of symmetry

1/5

Determine if there is a vertical line of symmetry

Determine if there is a horizontal line of symmetry

Determine if there is any diagonal lines of symmetry

Yes

Yes

No

Answer: no symmetry

1/5

Draw figure then determine whether the figure has line symmetry. If it does, draw all lines of symmetry. If it has no line symmetry, say “no symmetry”

Answer: One line of symmetry

2/5

Draw figure then determine whether the figure has line symmetry. If it does, draw all lines of symmetry. If it has no line symmetry, say “no symmetry”

Determine if there is a vertical line of symmetry Yes

Determine if there is a horizontal line of symmetry No

Determine if there is any diagonal lines of symmetry No

Answer: Two lines of symmetry.

2/5

Draw figure then determine whether the figure has line symmetry. If it does, draw all lines of symmetry. If it has no line symmetry, say “no symmetry”

Answer: No line symmetry

3/5

Draw figure then determine whether the figure has line symmetry. If it does, draw all lines of symmetry. If it has no line symmetry, say “no symmetry”

Determine if there is a vertical line of symmetry No

Determine if there is a horizontal line of symmetry No

Determine if there is any diagonal lines of symmetry No

Answer: One line of symmetry

3/5

Draw figure then determine whether the figure has line symmetry. If it does, draw all lines of symmetry. If it has no line symmetry, say “no symmetry”

Quadrilateral QRST has vertices Q(–1, 1), R(0, 3), S(3, 2), and T(4, 0). Find the coordinates of QRST after a reflection over the x-axis. Then graph both figures

4/5

                   

                   

                   

                   

                   

                   

                   

                   

                   

                   

Plot the 4 coordinates

Q(-1, 1)

R(0, 3)

S(3, 2)

T(4, 0)

Label Q

Label R

Label S

Label T

Q

RS

T

Connect the dots in order that was plotted

Quadrilateral QRST has vertices Q(–1, 1), R(0, 3), S(3, 2), and T(4, 0). Find the coordinates of QRST after a reflection over the x-axis. Then graph both figures

4/5

                   

                   

                   

                   

                   

                   

                   

                   

                   

                   

Identify the line of reflection

Q

RS

Tx-axis

Quadrilateral QRST has vertices Q(–1, 1), R(0, 3), S(3, 2), and T(4, 0). Find the coordinates of QRST after a reflection over the x-axis. Then graph both figures

4/5

                   

                   

                   

                   

                   

                   

                   

                   

                   

                   

Q

RS

T

Copy reflection

Begin with Q and count how far it is from the line of reflection (x-axis)

It is 1 unit from the line of reflection

Plot Q’ 1 unit on the other side of the line of reflection

Label Q’

Q’

Quadrilateral QRST has vertices Q(–1, 1), R(0, 3), S(3, 2), and T(4, 0). Find the coordinates of QRST after a reflection over the x-axis. Then graph both figures

4/5

                   

                   

                   

                   

                   

                   

                   

                   

                   

                   

Q

RS

T

Begin with R and count how far it is from the line of reflection (x-axis)

It is 3 units from the line of reflection

Plot R’ 3 units on the other side of the line of reflection

Label R’

Q’

R’

Quadrilateral QRST has vertices Q(–1, 1), R(0, 3), S(3, 2), and T(4, 0). Find the coordinates of QRST after a reflection over the x-axis. Then graph both figures

4/5

                   

                   

                   

                   

                   

                   

                   

                   

                   

                   

Q

RS

T

Begin with S and count how far it is from the line of reflection (x-axis)

It is 2 units from the line of reflection

Plot S’ 2 units on the other side of the line of reflection

Label S’

Q’

R’S’

Quadrilateral QRST has vertices Q(–1, 1), R(0, 3), S(3, 2), and T(4, 0). Find the coordinates of QRST after a reflection over the x-axis. Then graph both figures

4/5

                   

                   

                   

                   

                   

                   

                   

                   

                   

                   

Q

RS

T

Begin with T and count how far it is from the line of reflection (x-axis)

It is 0 units from the line of reflection

Plot T’ 0 units on the other side of the line of reflection

Label T’

Q’

R’S’

T’

Quadrilateral QRST has vertices Q(–1, 1), R(0, 3), S(3, 2), and T(4, 0). Find the coordinates of QRST after a reflection over the x-axis. Then graph both figures

4/5

                   

                   

                   

                   

                   

                   

                   

                   

                   

                   

Q

RS

T

Q’

R’S’

T’

Connect the new lines in order

Answer:

Quadrilateral ABCD has vertices A(–3, 2), B(–1, 5), C(3, 3), and D(2, 1). Find the coordinates of ABCD after a reflection over the x-axis. Then graph the figure and its reflected image.

Answer:

4/5

Triangle XYZ has vertices X(1, 2), Y(2, 1), and Z(1, –2). Find the coordinates of XYZ after a reflection over the y-axis. Then graph the figure and its reflected image.

5/5

                   

                   

                   

                   

                   

                   

                   

                   

                   

                   

Plot the 3 coordinates

X(1, 2)

Y(2, 1)

Z(1, -2)

Label X

Label Y

Label Z

X

Y

ZConnect the dots in order that was plotted

Triangle XYZ has vertices X(1, 2), Y(2, 1), and Z(1, –2). Find the coordinates of XYZ after a reflection over the y-axis. Then graph the figure and its reflected image.

5/5

                   

                   

                   

                   

                   

                   

                   

                   

                   

                   

X

Y

Z

Identify the line of reflection

y-axis

Triangle XYZ has vertices X(1, 2), Y(2, 1), and Z(1, –2). Find the coordinates of XYZ after a reflection over the y-axis. Then graph the figure and its reflected image.

5/5

                   

                   

                   

                   

                   

                   

                   

                   

                   

                   

X

Y

Z

Copy reflection

Begin with X and count how far it is from the line of reflection (y-axis)

It is 1 unit from the line of reflection

Plot X’ 1 unit on the other side of the line of reflection

Label X’

X’

Triangle XYZ has vertices X(1, 2), Y(2, 1), and Z(1, –2). Find the coordinates of XYZ after a reflection over the y-axis. Then graph the figure and its reflected image.

5/5

                   

                   

                   

                   

                   

                   

                   

                   

                   

                   

X

Y

Z

Begin with Y and count how far it is from the line of reflection (y-axis)

It is 2 units from the line of reflection

Plot Y’ 2 units on the other side of the line of reflection

Label Y’

X’

Y’

Triangle XYZ has vertices X(1, 2), Y(2, 1), and Z(1, –2). Find the coordinates of XYZ after a reflection over the y-axis. Then graph the figure and its reflected image.

5/5

                   

                   

                   

                   

                   

                   

                   

                   

                   

                   

X

Y

Z

Begin with Z and count how far it is from the line of reflection (y-axis)

It is 1 unit from the line of reflection

Plot Z’ 1 unit on the other side of the line of reflection

Label Z’

X’

Y’

Z’

Triangle XYZ has vertices X(1, 2), Y(2, 1), and Z(1, –2). Find the coordinates of XYZ after a reflection over the y-axis. Then graph the figure and its reflected image.

5/5

                   

                   

                   

                   

                   

                   

                   

                   

                   

                   

X

Y

Z

X’

Y’

Z’

Connect the new lines in order

Answer:

Triangle QRS has vertices Q(3, 4), R(1, 0), and S(6, 2). Find the coordinates of QRS after a reflection over the y-axis. Then graph the figure and its reflected image.

Answer:

*

5/5

Assignment

Lesson 10:9 Reflections 3 - 14 All