1. Chapter 1: Essentials of Geometry
Section 1.3: Use Midpoint and Distance Formulas

2. Section 1.3: Use Midpoint and Distance Formulas
Goals: Bisect a segment. Find the coordinates of the midpoint of a segment.

3. Section 1.3: Use Midpoint and Distance Formulas
Midpoint of a segment: the point that divides the segment into two congruent segments. Segment Bisector: a point, line, segment, ray, or plane that intersects the segment at its midpoint. To bisect (verb) a segment means to divide the segment into two congruent segments.

4. Section 1.3: Use Midpoint and Distance Formulas
Use algebra with segment lengths. 1. D is the midpoint of AM. If AD = 2x and DM = 50, find x and the length of AM. A D M

5. Section 1.3: Use Midpoint and Distance Formulas
Point A is the midpoint of CT. IF CA = 3x – 4 and AT = 5x – 26, find the value of x and the length of all of the segments
Segment DG bisects JB. If JO = 5x – 9,
OB = 4x + 15, DO = 3x – 8, and OG = 2x + 16, what are the lengths of all of the segments? Also, determine if JB bisects DG. C A T D O G J B

6. Section 1.3: Use Midpoint and Distance Formulas
Midpoint formula (on a number line) The midpoint of a segment on a number line is the average of the endpoints’ coordinates. |x1 – x2| 2 Example: Find the coordinate of the midpoint of AB if the coordinate of A is -6 and the coordinate of B is 5 Find the coordinate of the midpoint of CD if the coordinate of C is -11 and the coordinate of D is -3 x1 x2

7. Section 1.3: Use Midpoint and Distance Formulas
Midpoint formula (on a coordinate plane) The coordinates of the midpoint of a segment on a coordinate plane are the averages of the x-coordinate and of the y-coordinates of the endpoints. If point A is (x1, y1) and B is (x2, y2) the the midpoint M is: Handout on Midpoints

8. Section 1.3: Use Midpoint and Distance Formulas
The Distance Formula: Use the distance formula to find the distance between the following points: A (-2, -9) B (5, -1)

9. Section 1.3: Use Midpoint and Distance Formulas
Draw AB and CD so that they intersect, but neither segment bisects the other.
Draw AB and CD so that CD bisects AB, but AB does not bisect CD.
Draw AB and CD so that they bisect each other.
Draw AB and CD so that AB and CD do not intersect, but AB and CD do intersect.

10. Section 1.3: Use Midpoint and Distance Formulas
Homework: Pg. 19 #2-22 (even), #31-33 (all)