Geometry warm-up1. What is the name of the point in a triangle where all the

perpendicular bisectors meet?Circumcenter

2. What is the name of the point in a triangle where all the angle bisectors meet?

Incenter3. S is between points B and D. BD = 54 and SD = 13.9. Make a

sketch and tell the length of BS.BS = 40.1

4. What is the difference between an inscribed circle and a circumscribed circle of a triangle? (Name TWO characteristics of EACH circle that is different. You should have 4 listed all together.) Inscribed is inside and made with angle bisectorsCircumscribed in outside and made with perpendicular bisectors.

5. When an angle bisector is created, what is bisected?The angle

6. When a perpendicular bisector is created, what is bisected?A segment

1.7 Motion in the Coordinate Plane

Last time we talked about 3 rigid transformations. Name them and the motion associated with each.

1. Translation …..

Slides

2. Rotation …..

Turns

3. Reflection …..

Flips

Today

♥ Today, we’re going to talk about those same rigid transformations in the coordinate plane. This is called Coordinate Geometry.

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

♥ (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 to hand out

♥ Graph paper♥ Straight edges

♥ Activity 1– Translation♥ Activity 2 – Reflection♥ Activity 3 - Rotation

Notes on Activities

♥ 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

•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 and 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.

Assignment

♥ Pg 64, 9-17 odds, 23-30 all