1. Find the value of x and BC if B is between C and D, CB = 2x, BD = 4x, and BD = 12.
Problem of the Day

2. Section 1-3 Distance and Midpoints

3. Then Now Objectives You graphed points on the coordinate plane.
Find the distance between two points.
Find the midpoint of a segment.

4. Common Core State Standards
Content Standards
Common Core State Standards
G.CO.1 – Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment, based on the undefined notations of point, line, distance along a line, and distance around an arc. G.CO.12 – Make formal geometric constructions with a variety of tools and methods.
Mathematical Practices
2) Reason abstractly and quantitatively. 7) Look for and make use of structure.

5. The distance between two points is the length of the segment with those points as its endpoints.
Vocabulary

6. Distance Formula (on a number line)

7. Example 1
Use the number line to find each measure. AC C FB

8. Irrational Number: a number that cannot be expressed as a terminating or repeating decimal.
Vocabulary

9. Distance Formula (in Coordinate Plane)

10. Distance Formula Continued

11. Find the distance between the pair of points. E(-5, 6) and F(8, -4)
Example 2

12. Find the distance between the pair of points. J(4, 3) and K(-3, -7)
Example 2

13. Find the distance between the pair of points. E(-4, 1) and F(3, -1)
Example 2

14. The midpoint of a segment is the point halfway between the endpoints of the segment.
Vocabulary

15. Midpoint Formula (on a number line)

16. Marco places a couch so that its end is perpendicular and 2
Marco places a couch so that its end is perpendicular and 2.5 feet away from the wall. The couch is 90” wide. How far is the midpoint of the couch from the wall in feet?
Example 3

17. The temperature on a thermometer dropped from a reading of 25° to -8 °
The temperature on a thermometer dropped from a reading of 25° to -8 °. Find the midpoint of these temperatures.
Example 3

18. Midpoint Formula (in Coordinate Plane)

19. Find the coordinates of the midpoint of a segment with the given coordinates. A(5, 12) and B(-4, 8) C(-8, -2) and D(5, 1) E(8, -6) and F(-14, 12)
Example 4

20. Find the coordinates of the missing endpoint if P is the midpoint of 𝐸𝐺 . E(-8, 6) and P(-5, 10) P(-1, 3) and G(5, 6) P(-6, 4) and G(-5, -3)
Example 5

21. Find YZ if Y is the midpoint of 𝑋𝑍 and XY = 2x – 3 and YZ = 27 – 4x.
Example 6

22. Find PR if Q is the midpoint of 𝑃𝑅 and QR = 6 – 3x and PR = 14x + 2.
Example 6

23. Find the value of x if C is the midpoint of 𝐴𝐵 , AC = 4x + 5, and AB = 78.
Example 6

24. p.30 #3-6, 40, 42, 44, 48, 50, 54, 56 ,68
Homework