Lesson 10-9 Pages Reflections

What you will learn! How to identify figures with line symmetry and graph reflections on a coordinate plane.

Line Symmetry Line of symmetry Reflection

What you really need to know!

A type of transformation where a figure is flipped over a line of symmetry is a reflection.

What you really need to know! To draw the reflection of a polygon, find the distance from each vertex of the polygon to the line of symmetry. Plot the new vertices the same distance from the line of symmetry but on the other side of the line. Then connect the new vertices to complete the reflected image.

Example 1: Determine whether each figure has a line of symmetry. If so, copy the figure and draw all the lines of symmetry.

Example 2: Determine whether each figure has a line of symmetry. If so, copy the figure and draw all the lines of symmetry.

Example 3: Determine whether each figure has a line of symmetry. If so, copy the figure and draw all the lines of symmetry. No symmetry

Example 4: 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 the figure and its reflected image.

RQ S T R’ Q’ S’ T’ Q (-1,1) R (0,3) S (3,2) T (4,0) Q’ (-1,-1) R’ (0,-3) S’ (3,-2) T’ (4,0)

Vertices of Quadrilateral QRST Distance from x- axis Vertices of Quadrilateral QRST Q(–1, 1) 1 Q’ (-1,-1) R(0, 3) 3 R’ (0,-3) S(3, 2) 2 S’ (3,-2) T(4, 0) 0 T’ (4,0)

Example 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.

X Y Z Y’ X’ Z’ X (1,2) Y (2,1) Z (1,-2) X’ (-1,2) Y’ (-2,1) Z’ (-1,-2)

Vertices of  XYZ Distance from y-axis Vertices of  XYZ X(1, 2) 1 X’ (-1,2) Y(2, 1) 2 Y’ (-2,1) Z(1, –2) 1 Z’ (-1,-2)

Page 458 Guided Practice #’s 3-6

A (5,8) B (1,2) C (6,4)

W (-4,-2) X (-4,-3) Y (-2,4) Z (-2,-1)

Pages with someone at home and study examples! Read:

Homework: Page #’s 7-17 all #’s all Lesson Check Ch 10

F E D (-3,6) E (-2,-3) F (2,2) G (4,9)

T UVT’ U’V’ T (-6,1) U (-2,-3) V (5,-4)

Q (2,-5) R (4,-5) S (2,3) Q’ (-2,-5) R’ (-4,-5) S’ (-2,3)

H I J K J’ I’ H’ K’ H (-1,3) I (-1,-1) J (2,-2) K (2,2) H’ (1,3) I’ (1,-1) J’ (-2,-2) K’ (-2,2)

Study Guide and Review Pages #’s 6-22 (Odd answers in back of book)

Prepare for Test! Page 465 #’s 1-16

Prepare for Test! Pages #’s 1-17