Reflections on the Coordinate Plane

Reflections on the Coordinate Plane

• The undisturbed surface of a pond acts like a mirror and can provide the subject for beautiful photographs

Reflections on the Coordinate Plane

• We call the waterline a “line of symmetry” because if the photo were folded at the waterline, the two halves would form a mirror image of each other

Reflections on the Coordinate Plane

• Similarly, the x or y-axis can act as a line of symmetry on the coordinate plane.

Reflections Mini-Lab• Count how many units point A is from the x-axis.

Then count that many units on the opposite side of the x-axis and label this point A’

C

A B

3 units

3 unitsA’

Reflections Mini-Lab• Count how many units point B is from the x-axis.

Then count that many units on the opposite side of the x-axis and label this point B’

C

A B

1 unit

1 unitB’

A’

Reflections Mini-Lab• Count how many units point C is from the x-axis.

Then count that many units on the opposite side of the x-axis and label this point C’

C

A B

5 units

5 units

C’

A’

B’

Reflections Mini-Lab• Draw triangle A’B’C’• What do you notice about the two

triangles? C

A B

C’

A’

B’

Triangle A’B’C’ is a reflection of triangle ABC

Reflections Mini-Lab• Compare the coordinates of A with A’, B

with B’, and C with C’• What pattern do you notice?

C

A B

C’

A’

B’

A (1, 3)B (5, 1)C (3, 5)

A’ (1, -3)B’ (5, -1)C’ (3, -5)

Same x value, Opposite y value

Reflections Mini-Lab• The reflection in this mini-lab is a reflection

over the x-axis. • The x-axis acts as the line of symmetry

C

A B

C’

A’

B’

A (1, 3)B (5, 1)C (3, 5)

A’ (1, -3)B’ (5, -1)C’ (3, -5)

Reflections Mini-Lab• To reflect a figure over the x-axis, use the

same x-coordinate and multiply the y-coordinate by -1

C

A B

C’

A’

B’

A (1, 3)B (5, 1)C (3, 5)

A’ (1, -3)B’ (5, -1)C’ (3, -5)

Reflections Mini-Lab• What do you think would happen if we

multiplied the original x-coordinate by -1 and used the same y-coordinate?

C

A B

C’

A’B’

A (1, 3)B (5, 1)C (3, 5)

A’ (-1, 3)B’ (-5, 1)C’ (-3, 5)

You create a reflection over the y-axis!

Reflections Mini-Lab

What did we learn?• To reflect a figure over the x-axis, use

the same x-coordinate and multiply the y-coordinate by -1

• To reflect a figure over the y-axis, multiply the x-coordinate by -1 and use the same y-coordinate

Reflections on the Coordinate Plane Checkpoint

• If square MATH is reflected into quadrant II, what is the line of symmetry?

The y-axisM A

H T

Reflections on the Coordinate Plane Checkpoint

• What are the coordinates of square MATH when reflected over the y-axis?

M’ (-1, 4)M A

H T A’ (- 4, 4)

T’ (-4, 1)

H’ (- 1, 1)

Reflections on the Coordinate Plane Checkpoint

• If square MATH is reflected into quadrant IV, what is the line of symmetry?

The x-axisM A

H T

Reflections on the Coordinate Plane Checkpoint

• What are the coordinates of square MATH when reflected over the x-axis?

M’ (1,- 4)M A

H T A’ (4,- 4)

T’ (4,- 1)

H’ (1,- 1)

Homework

• Practice Worksheet 11-9• Practice Skills 6-7• Due Tomorrow!!