Presentation on theme: "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."— Presentation transcript:
1 Geometry warm-upWhat is the name of the point in a triangle where all the perpendicular bisectors meet?CircumcenterWhat is the name of the point in a triangle where all the angle bisectors meet?IncenterS is between points B and D. BD = 54 and SD = Make a sketch and tell the length of BS.BS = 40.1What 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 angle6. When a perpendicular bisector is created, what is bisected?A segment
2 1.7 Motion in the Coordinate Plane Last time we talked about 3 rigid transformations. Name them and the motion associated with each.Translation …..SlidesRotation …..Turns3. Reflection …..Flips
3 TodayToday, we’re going to talk about those same rigid transformations in the coordinate plane. This is called Coordinate Geometry.
4 Whatever transformation occurred: moved the x-coordinate 2 units to the right (positive)and the y-coordinate 4 units up (positive).
5 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)
6 Activities Volunteers to hand out Graph paper Straight edges Activity 1– TranslationActivity 2 – ReflectionActivity 3 - Rotation
10 Notes on Activities Translations ADD the same number (positive or negative) to each of the x-coordinatesand the same number (could be different from the x-axis addend) to each y-coordinate.The image is congruent to the pre-image
11 Reflections –MULTIPLY the x-coordinate by -1 to reflect across the y-axisMULTIPLY the y-coordinate by -1 to reflect across the x-axisfor 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°
12 RotationsMULTIPLY 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.