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1. The Distance Between Points of a number line

2. Objective: DETERMINE THE DISTANCE BETWEEN TWO POINTS ON A NUMBER LINE USING THE FORMULA DISTANCE = |X₂ − X₁|

3. IN ANALYTIC GEOMETRY, WE LOCATE POINTS ON A COORDINATE SYSTEM. A NUMBER LINE IS A 1D COORDINATE SYSTEM. THE DISTANCE BETWEEN ANY TWO POINTS, X₁ AND X₂ ​, IS GIVEN BY: {DISTANCE} = | X₂ − X₁ | THIS FORMULA ENSURES THAT DISTANCE IS ALWAYS NON-NEGATIVE.

4. Find the distance between x=3 and x=−4. Find the distance between x=−2 and x=5. Find the distance between x=−7 and x=2. Examples:

5. 4. What is the distance from x=a to x=a + h? 5. X₁ =a , X₂ =a+9, find the distance. 6. X₁ =𝑏−2, X₂ =𝑏+5, find the distance. Examples:

6. The midpoint Formula

7. Objectives: Derive and apply the Midpoint Formula in 2D space. Interpret the midpoint geometrically and algebraically. Solve real-world and abstract problems involving midpoints

8. Midpoint and Distance in the Coordinate Plane You can use formulas to find the midpoint and the length of any segment in the coordinate plane. Number Line Coordinate Plane

9. Segment AB has endpoints at -4 and 9. What is the coordinate of its midpoint? Examples:

10. Examples:

11. Segment EF has endpoints E (7 , 5) and F (2 , -4). What are the coordinates of its midpoint M?

12. If the coordinate (2, -3) is the midpoint of line AB and the endpoint A is (5, 4), what is the missing coordinate B? (-1, -10)

13. Find the midpoint of the segment given the endpoints (5, 7) and (13, 1). What is the midpoint of the line segment with endpoints (–3, –3) and (7, 3)? Line segment CD has a midpoint at (1, 2). If endpoint C is located at (–5, 3), find the ordered pair represented the other endpoint D. Try This: