Reflections on the Coordinate Plane Reflections on the

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 3 units A’ 3 units B

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 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 5 units A B B’ A’ 5 units C’

Reflections Mini-Lab • Draw triangle A’B’C’ • What do you notice about the two Triangle A’B’C’ is a triangles? 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) A’ (1, -3) B (5, 1) B’ (5, -1) C (3, 5) 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) A’ (1, -3) B (5, 1) B’ (5, -1) C (3, 5) 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 ycoordinate by -1 C A B A (1, 3) A’ (1, -3) B (5, 1) B’ (5, -1) C (3, 5) 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 A (1, 3) A’ (-1, 3) B (5, 1) B’ (-5, 1) C (3, 5) C’ (-3, 5) 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? M A T H The y-axis

Reflections on the Coordinate Plane Checkpoint • What are the coordinates of square MATH when reflected over the y-axis? M T A H M’ (-1, 4) A’ (- 4, 4) T’ (-1, 1) H’ (- 4, 1)

Reflections on the Coordinate Plane Checkpoint • If square MATH is reflected into quadrant IV, what is the line of symmetry? M A T H The x-axis

Reflections on the Coordinate Plane Checkpoint • What are the coordinates of square MATH when reflected over the x-axis? M T A H M’ (1, - 4) A’ (4, - 4) T’ (1, - 1) H’ (4, - 1)

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