Introduction and Review Information

Example Pre-Image Image A' A B B' C' C

Remember equations for horizontal lines: Writing Equations Remember equations for horizontal lines: y = 2 is horizontal line crossing y-axis at 2 y = –4 is horizontal line crossing y-axis at 4 y=2 y =–4

Remember equations for vertical lines: Writing Equations Remember equations for vertical lines: x = 2 is vertical line crossing x-axis at 2 x = –4 is vertical line crossing x-axis at –4 x=2 x =–4

Reflections 12-1 I CAN - Accurately reflect a figure in space. - Reflect a figure across the x-axis, the y-axis the line y = x, or the line y = –x Holt Geometry

Recall that a reflection is a transformation that moves a figure (the preimage) by flipping it across a line.

Example 1: Identifying Reflections Tell whether each transformation appears to be a reflection. Explain. A. B. No; the image does not Appear to be flipped. Yes; the image appears to be flipped across a line..

Reflecting across vertical lines (x = a) Reflect across x = 2 Step 1 – Draw line of reflection A B B' A' Step 2 – Pick a starting point, count over-ALWAYS vertically or horizontally to line D C C' D' Step 3 – Go that same distance on the other side of line Step 4 – LABEL THE NEW POINTS Step 5 – Continue with other points

Reflecting across y-axis Pre-image Image C'(3, 7) C A T C’ C(-3, 7) A(-3, 2) A'(3, 2) A’ T’ T(2, 2) T'(-2, 2) What do you notice about the x and y coordinates of the pre-image and image points?

Reflecting across x-axis Reflect the following shape across the x-axis Pre-image Image M(2, 1) M’(2, -1) A(-1, 1) A’(-1, -1) T H T(-3, 5) T’(-3, -5) A M H(4, 5) H’(4, -5) A’ M’ T’ H’ What do you notice about the x and y coordinates of the pre-image and image points?

Reflecting across the line y = x Pre-Image Image F(-3, 0) F‘(0, -3) I(4, 0) I’ S’ I'(0, 4) S(4, -9) F I S'(-9, 4) F’ H(-3, -9) H'(-9, -3) H’ What do you notice about the x and y coordinates of the pre-image and image points? H S

8. Reflect across y = –x M(-5, 2) O(-2, 2) V(0, 6) E(-7, 6)

8. Reflect across y = -3 H’(-12, 2) A’(7, -7) T’(2, -7) H T A

Reflect the rectangle with vertices S(3, 4), Check It Out! Reflect the rectangle with vertices S(3, 4), T(3, 1), U(–2, 1) and V(–2, 4) across the x-axis. The reflection of (x, y) is (x,–y). S(3, 4) S’(3, –4) V S U T T(3, 1) T’(3, –1) U(–2, 1) U’(–2, –1) V’ S’ U’ T’ V(–2, 4) V’(–2, –4) Graph the image and preimage.