Section 9-1 Reflections

Then Now Objectives You identified reflections and verified them as congruence transformations. Draw reflections. Draw reflections in the coordinate plane.

Common Core State Standards Content Standards G.CO.4 – Develop definitions of rotations, reflections, and translations in terms of angles, circles, perpendicular lines, parallel lines, and line segments. G.CO.5 – Given a geometric figure and a rotation, reflection, or translation, draw the transformed figure. Specify a sequence of transformations that will carry a given figure onto another. Mathematical Practices 5) Use appropriate tools strategically. 7) Look for and make use of structure. Common Core State Standards

A transformation is an operation that maps and original geometric figure, the preimage, onto a new figure called the image. A transformation can change the position, size, or shape of a figure. Vocabulary

A reflection or flip is a transformation over a line called the line of reflection. Each point of the preimage and its image are the same distance from the line of reflection. Vocabulary

Copy the figure and the given line of reflection Copy the figure and the given line of reflection. Then draw the reflected image in this line. Example 1

Copy the figure and the given line of reflection Copy the figure and the given line of reflection. Then draw the reflected image in this line. Example 1

Trapezoid RSTV has vertices R(-1, 1), S(4, 1), T(4, -1), and V(-1, -3) Trapezoid RSTV has vertices R(-1, 1), S(4, 1), T(4, -1), and V(-1, -3). Graph trapezoid RSTV and its image in the line y = -3. Example 3

Trapezoid RSTV has vertices R(-1, 1), S(4, 1), T(4, -1), and V(-1, -3) Trapezoid RSTV has vertices R(-1, 1), S(4, 1), T(4, -1), and V(-1, -3). Graph trapezoid RSTV and its image in the line x = 2. Example 3

Graph the figure and its image under the given reflection: Triangle ABC with vertices A(-5, 3), B(2, 0), and C(1, 2) in the x-axis. Example 4

Graph the figure and its image under the given reflection: Parallelogram with vertices P(-4, 1), Q(2, 3), R(2, -1), and S(-4, -3) in the y-axis. Example 4

Graph the figure and its image under the given reflection: Rectangle with vertices E(-4, -1), F(2, 2), G(3, 0), and H(-3, -3) in the x-axis. Example 4

Graph the figure and its image under the given reflection: Triangle JKL with vertices J(3, 2), K(2, - 2), and L(4, -5) in the y-axis. Example 4

Quadrilateral JKLM has vertices J(2, 2), K(4, 1), L(3, -3), and M(0, -4). Graph JKLM and its image J’K’L’M’ in the line y = x. Example 5

Triangle BCD has vertices B(-3, 3), C(1, 4), and D(-2, -4) Triangle BCD has vertices B(-3, 3), C(1, 4), and D(-2, -4). Graph triangle BCD and its image in the line y = x. Example 5

p.627 #1, 3, 19 – 29 odd, 45 Homework