1. Chapter 1: Tools of Geometry
Lesson 3: Distance and Midpoint
Chapter 1: Tools of Geometry

2. Midpoint- the point on a segment that divides the segment into two congruent segments
Segment bisector- any line, segment or plane that intersects a segment at its midpoint
Definitions

3. Distance Formula- used to find the length of a segment.
ex: Find the distance between
A (5,1) and B (-3, -3).
*on a number line- subtract the endpoint values
Midpoint Formula- used to find the point half way down a segment
ex: Find the midpoint of JK if
J(-1,2) and K(6, 1)
* on a number line- add the endpoint values and divide by 2
Distance and Midpoint

4. Use the number line to find the midpoint and the measure of AX.
examples

5. Find the midpoint and distance between E(–4, 1) and F(3, –1).
Examples

6. Find the distance and midpoint of AM
Examples

7. Find the coordinates of R if N (8, –3) is the midpoint of RS and S has coordinates (–1, 5).
Examples

8. Examples

9. Find LM. Assume that the figure is not drawn to scale.
Examples

10. Find the value of x and ST if T is between S and U, ST = 7x, SU = 45, and TU = 5x – 3.
Examples

11. Find the value of n and WX if W is between X and Y, WX = 6n – 10, XY = 17, and WY = 3n.
Examples