9.1 Reflections By: The Tortellini's Draga, Kristin, Saahithi

Objectives  Identifying and drawing reflections.  Reflections in the coordinate plane.

Vocabulary  Isometry: A transformation that does not change the shape or size of a figure, also known as congruence transformations or rigid transformations.  Reflection: A transformation that moves a figure by flipping it across a line.  Preimage : The figure before it is flipped over the line.  Image: The figure once it is flipped or reflected over the line.

Identifying Reflections  A transformation is a reflection if it appears to be flipped across a line.

Examples of Reflections A. Not a reflection because B. This is a reflection. the image is not flipped because the image over a line. is flipped over the line.

More on Reflections  A reflection is a transformation across a line, called the line of reflection, so that line of reflection is the perpendicular bisector of each segment joining each point and its image.

Steps in drawing reflections 1. Copy the quadrilateral and the line of reflection. 2. Draw the reflection of the quadrilateral across the line. 3. Through each line draw a line perpendicular to the line of reflection. 4. Measure the distance from each vertex to the line of reflection. Locate the image of each vertex on the opposite side of the line of reflection and the same distance from it. 5. Connect the images of the vertices.

Word problem with a reflection being drawn  A trail designer is planning two trails that connect campsites A and B to a point on the river. He wants the total length of the trails to be as short as possible. Where should the trail meet the river?

Reflections in the coordinate plane Across the x-axis Across the y-axis Across the line y = x

Drawing reflections in the coordinate plane  Reflect the figure with the given vertices across the give line. Example #1 M(1,2),N(1,4),P(3,3):y-axis The reflection of (x,y) is (-x,y).

Drawing reflections in the coordinate plane  Example #2 D(2,0),E(2,2),F(5,2),G(5,1);y = x The reflection of (x,y) is (y,x).