1. Unit 01 – Lesson 03 – Distance & Length
Calculate with measures
Find the distance between two points.
Find the midpoint of a segment
Locate a point on a segment given a fractional distance from one endpoint.

2. Ruler Postulate (Card #8)
The points on a line can be matched one to one with the real numbers. The real number that corresponds to a point is the coordinate of the point. The distance between points A and B, written as AB, is the absolute value of the difference of the coordinates of A and B.

6. Betweeness
When three points are collinear, you can say that one point is between the other two.

7. Segment Addition Postulate (Card #9)
If B is between A and C, then AB + BC = AC If AB + BC = AC, then B is between A and C.

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

10. Congruent Segments
Line segments that have the same length are called congruent segments.
You can say “the length of AB is equal to the length of CD,” or you can say “AB is congruent to CD.”
The symbol ≅ means “is congruent to”

11. ( 𝑥 2 − 𝑥 1 ) 2 + ( 𝑦 2 − 𝑦 1 ) 2 Distance Formula
If A(x1, y1) and B(x2, y2) are points in a coordinate plane, then the distance between A and B is:
( 𝑥 2 − 𝑥 1 ) 2 + ( 𝑦 2 − 𝑦 1 ) 2

12. Find the distance between E(–4, 1) and F(3, –1).

13. Find the distance between A(–3, 4) and M(1, 2).

14. Midpoints
The midpoint of a segment is the point that divides the segment into two congruent segments.

15. Segment Bisectors
A segment bisector is a point, ray, line, or line segment, or plane that intersects the segment at its midpoint. A midpoint or segment bisector bisects a segment.

18. Partitioning a segment on a number line
For a segment 𝐽𝐾 with endpoints at coordinates 𝑥 1 and 𝑥 2 , the point P with coordinate 𝑎𝑥 1 + 𝑏𝑥 2 𝑎+𝑏 partitions the segment in the ratio b:a.

20. Midpoint formula on a number line
If 𝐴𝐵 has endpoints 𝑥 1 and 𝑥 2 on a number line, then the midpoint M of 𝐴𝐵 , has coordinate 𝑥 1 + 𝑥 2 2

21. DECORATING Marco places a couch so that its end is perpendicular and 2
DECORATING 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 back from the wall in feet?

22. Midpoint formula on a coordinate plane
The coordinates of the midpoint of a segment are the averages of the x-coordinates and of the y- coordinates of the endpoints. If A(x1, y1) and B(x2, y2) are points in a coordinate plane, then the midpoint M of 𝐴𝐵 has coordinates M = ( 𝑥 1 + 𝑥 2 2 , 𝑦 1 + 𝑦 2 2 )

23. Find the coordinates of M, the midpoint of 𝐺𝐻 for G(8, -6) and H(-14, 12).

24. Find the coordinates of D if E(-6, 4) is the midpoint of 𝐷𝐹 and F has coordinates (-5, -3)

25. Find X on 𝐵𝐷 that is 1 4 the distance from B to D.

26. Find P on 𝑁𝑀 that is 1 3 of the distance from N to M.