Geometry
Practice – Segments, Midpoint, & Distance
Name_______________________________
1. Point S is between R and T on RT . Use the given information to write an equation in terms of x. Solve
the equation. Then find RS and ST.
RS = 2x + 10
ST = x – 4
RT = 21
2. Given that M is the midpoint, find PR.
10x - 51
6x - 11
P
M
R
3. Find the coordinates of the midpoint if the endpoints of the segment are E(0, 4) and F(4, 3).
4. Use the given endpoint R and the midpoint M of RS to find the coordinates of the other endpoint S.
R(5, 1), M(1, 4)
Solve each equation.
5. 9x + 2x + 6 – x = 10
6. 5x – 22 – 7x + 2 = 40
Questions 7 – 10: Use the diagram at the right.
7. Name two rays with endpoint B.
A
B
P
8. Name three rays that contain point C.
D
C
9. Name the intersection of AB and BC.
Q
E
10. If plane P and plane Q never intersect, what do you know about them?
The Distance Formula
To find the length of a segment connecting two points (x1, y1) and (x2, y2) use the formula:
D=
 x 2  x1 
2
  y 2  y1 
2
Example: Find the distance between (7, 2) and (4, 6)
Let (7, 2) be (x1, y1) and (4, 6) be (x2, y2):
then:
D=
4  7
=
 3 
=
9  16
2
2
 6  2
 4
2
2
= 25
= 5 units
Find the distance between the points listed. Use the results to find the distance from the pitcher’s rubber to
the home plate in baseball. Remember, you must show all work … do not just write the answer in below!
1. (–2, –3) and (–2, 4)
6. (–2, 6) and (–10, –9)
2. (–7, 5) and (1, –1)
7. (2, –12) and (7, 0)
3. (–2, 3) and (3, –2)
8. (3, –2) and (5, –3)
4. (–6, –2) and (–7, –5)
9. (–4, 5) and (8, –4)
5. (–2, –1) and (–5, –5)
10. (2, 4) and (3, 5)
7
C
E
13
15
5
F
H
I
N
____ ____ ____ ____ _____
6
5
3
2
10
____ ____ ____
6
5
3
17
10
S
T
X
Y
____ ____ ____ ____ ,
7
8
8
2
____ ____ ____ ____ ____ ____
5
4
1
9
8
6