Geometry warm-up What is the name of the point in a triangle where all the perpendicular bisectors meet? Circumcenter What is the name of the point in.

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Geometry warm-up What is the name of the point in a triangle where all the perpendicular bisectors meet? Circumcenter What is the name of the point in a triangle where all the angle bisectors meet? Incenter 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 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 bisectors Circumscribed 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. Translation ….. Slides 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).

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 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