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Triangle has been reflected so that the vertices of its image are labeled points. What is the image of triangle ?
What specific information do you need to be able to solve the problem?
14 points on a circle with varying distances between them. Starting from the top center and moving clockwise, the points are labeled A, D, E, G, I, J, L, N, P, Q, R, T, U, and V.
Your teacher will give you either a problem card or a data card. Do not show or read your card to your partner.
If your teacher gives you the problem card:
If your teacher gives you the data card:
14 points on a circle with varying distances between them. Starting from the top center and moving clockwise, the points are labeled A, D, E, G, I, J, L, N, P, Q, R, T, U, and V.
Here are three congruent L shapes on a grid.
Think about reflecting the point across line :
The image is somewhere on the other side of from . The line is the boundary between all the points (not drawn) that are closer to and all the points that are closer to . In other words, is the set of points that are the same distance from as from . In a previous lesson, we conjectured that a set of points that are the same distance from as from is the perpendicular bisector of the segment . Using a construction technique from a previous lesson, we can construct a line perpendicular to that goes through :
lies on this new line at the same distance from as :
Line L, facing upward and to the left. A perpendicular line passes through Line l and Point A. A circle is drawn with the center as the right angle and Point A as the radius, passing through Point A prime.
We define the reflection across line as a transformation that takes each point to a point as follows: lies on the line through that is perpendicular to , is on the other side of , and is the same distance from as . If happens to be on line , then and are both at the same location (they are both a distance of zero from line ).
A reflection is a rigid transformation that is defined by a line. It takes one point to another point that is the same distance from the given line, but on the other side. The segment from the original point to its image is perpendicular to the line of reflection.
In this figure, is reflected across line , and is the image of under the reflection.
Reflect across line .