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 units A’

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 unit B’ 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 B’ 5 units A’ C’

Reflections Mini-Lab Draw triangle A’B’C’ What do you notice about the two triangles? Triangle A’B’C’ is a reflection of triangle ABC C A B B’ A’ C’

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 A (1, 3) B (5, 1) C (3, 5) A’ (1, -3) B’ (5, -1) C’ (3, -5) B’ Same x value, Opposite y value A’ C’

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

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

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’ C A B A (1, 3) B (5, 1) C (3, 5) A’ (-1, 3) B’ (-5, 1) C’ (-3, 5) A’ B’ 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-axis M 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-axis M 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