Name _______________________
WORKSHEET #3
Upward Bound Summer 2011: Geometry
OBJECTIVE:
I will be able to determine segment lengths using diagrams and the Segment Addition Postulate.
I will be able to find the distance between two points in the coordinate plane using the distance formula.
NEW CONCEPT:
New Vocabulary → Postulate, Segment Addition Postulate, midpoint
Say WHAT?
Geometry can be weird...
The Segment Addition Postulate:
“If AC = n, then AB + BC = n”
A
n
𝐴𝐶 means:
C
B
Midpoints:
̅̅̅̅
𝐴𝐶 means:
If point M is the midpoint of ̅̅̅̅ , then AM = MB
A
M
B
NOTES AND EXAMPLES:
Example 1: Point J is between points A and B on ̅̅̅̅
a)
If AJ = 8 and JB = 7, then AB = ____________
b)
If AB = 12 and JB = 4, then AJ = ____________
c)
If AJ = 8 and JB = 8, then point J is called the ____________ of ̅̅̅̅
Example 2: AC = 9. Solve for x and find the length of ̅̅̅̅ .
3x – 1
2x
A
C
B
Example 3: Point M is the midpoint of ̅̅̅̅. Solve for x and find the length of ̅̅̅̅ .
10x – 4
8x + 2
L
M
N
We can use the distance formula to find the distance between any two points in the coordinate
plane. In the formula below, d is distance and the two points are (x1 , y1) and (x2 , y2).
√
Example 4: Find the distance between the points (-2, 1) and (1, 5).
Example 5: Find the length of the line segment with endpoints (-2, 3) and (5, -3). Round to the
nearest tenth.
Example 6: Find how long each segment would be if it were drawn on the graph below. Round to the
nearest tenth if necessary.
a)
̅̅̅̅
A
b)
B
̅̅̅̅
C
c)
̅̅̅̅