4.2 Reflections.

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Presentation transcript:

4.2 Reflections

Ex. 1 horizontal and vertical reflections Graph triangle ABC with vertices A(1,3); B(5,2); C(2,1). Tell and graph image with reflection over x = 3. Draw in line and just count how far away from line of reflection and go opposite direction the same amount A’(5,3) left two, so go right 2 from line of reflection B’(1,2) left one, so go right one from line of reflection C’(4,1) right two, so go left two from line of reflection

Ex. 2 Reflecting when y = x When y = x then (a,b) → (b,a) What are coordinates for image of FG with endpoints F(-1,2) and G(1,2) when reflected over y = x F’(2,-1) G’(2,1)

Ex. 3 Reflecting over y = -x (a,b) → (-b,-a) Graph Quad with vertices A(-3,2); B(1,-1); C(-2,-2); D(-4,-1) and image reflected over y = -x A’(-2,3); B’(1,-1); C’(2,2); D’(1,4)

Ex. 4 glide reflections Image of a translation (glide) followed by a reflection (reflection) Graph ABC with vertices A(3,2); B(6,3); C(7,1) and image after a glide reflection of: Translation (x – 8, y) and reflected over x – axis Translation: A’(-5,2); B’(-2,3); C(-1,1) Reflection: A’’(-5,-2); B’’(-2,-3); C(-1,-1)

Your Practice Graph RST with vertices R(4,1); S(7,3); T(6,4) with translation of (x, y – 1) and reflected over y = x Give final coordinates of glide reflection and graph image Translation: R’(4,0); S’(7,2); T’(6,3) Reflection: R’’(0,4); S’’(2,7); T’’(3,6)

F Ex. 5 symmetry Flipping an image onto itself Line that does this is called the line of symmetry How many lines of symmetry? 2 None infinite F