Geometry warm-up Get a strip of paper from the back desk. Fold it in half, then half again. Draw a SpongeBob character in the first frame. Reflect it into the second frame. Reflect that one into the 3rd frame. Then,…. guess what?... Yep. Reflect that one into the 4th frame.

On a small piece of paper, write your name, then tell me the effect of a double reflection. Do not discuss this with anyone. Turn it in.

Let’s grade your homework Motion in geometry packet.

Motion in the Coordinate Plane

Last time we talked about 3 rigid transformations. Translation ….. Slides Rotation ….. Turns Reflection ….. Flips

Coordinate Geometry Today… Wait for it….. We’re going to talk about those same rigid transformations in the coordinate plane. This is called ... Coordinate Geometry Wait for it…..

Whatever transformation occurred: moved the x-coordinate 2 units to the right (positive) and the y-coordinate 4 units up (positive).

In our Geometry notation, we can write: T(x,y) = (x + 2, y + 4) (reminder) Whatever transformation occurred: moved the x-coordinate 2 units to the right (positive) and the y-coordinate 4 units up (positive). THIS SAME OPERATION HAPPENS ON EACH POINT. The result is an image that is congruent to the pre-image. In our Geometry notation, we can write: T(x,y) = (x + 2, y + 4) Read, “the transformation of a point (x,y) moved right 2 and up 4”

Activities Volunteers hand out Graph paper Straight edges

“What you should have learned” (write these down in your notebook) Translations ADD the same number (positive or negative) to each of the x-coordinates and the same number (could be different from the x-axis addend) to each y-coordinate. The image is congruent to the pre-image

You should have learned this, too (write these down in your notebook) Reflections – MULTIPLY the x-coordinate by -1 to reflect across the y-axis MULTIPLY the y-coordinate by -1 to reflect across the x-axis for a special reflection: MULTIPLY both coordinates by -1 to end up with a double reflection: across one axis and then the other. This is also considered a ROTATION of 180°

Rotations MULTIPLY each coordinate by -1 to rotate a figure 180° about the origin. Since rotations are based on degrees, there is no ‘rule’ regarding operations on a point.

Let’s Play Interactive Transformations in the Coordinate Plane

Assignment 16-3 Packet