NAME _____________________________________________ DATE ____________________________ PERIOD _____________
1-3 Study Guide and Intervention
Distance and Midpoints
Distance Between Two Points
Distance on a Number Line
Distance in the Coordinate Plane
Distance Formula:
d = √(𝑥2 − 𝑥1 )2 + (𝑦2 – 𝑦1 )2
AB = |𝑥1 – 𝑥2 | or |𝑥2 – 𝑥1 |
Example 2: Find the distance between A(–2, –1) and
Example 1: Use the number line to find AB.
B(1, 3). Distance Formula
d = √(𝑥2 − 𝑥1 )2 + (𝑦2 – 𝑦1 )2
AB = |(–4) – 2|
= |– 6|
AB = √(1 − (−2 ))2 + (3 − (−1))2
=6
AB = √(3)2 + (4)2
= √25
=5
Exercises
Use the number line to find each measure.
1. BD 6
2. DG
12
4. EF
9
3
5. BG 15
6. AG
17
7. BE
8. DE
1
3. AF
7
Find the distance between each pair of points.
9. A(0, 0), B(6, 8) 10
10. R(–2, 3), S(3, 15) 13
11. M(1, –2), N(9, 13) 17
12. E(–12, 2), F(–9, 6) 5
13. X(0, 0), Y(15, 20) 25
14. O(–12, 0), P(–8, 3)
15. C(11, –12), D(6, 2) √𝟐𝟐𝟏 ≈ 14.9
16. K(–2, 10), L(–4, 3)
Chapter 1
18
5
√𝟓𝟑 ≈ 7.3
Glencoe Geometry
NAME _____________________________________________ DATE ____________________________ PERIOD _____________
1-3 Study Guide and Intervention (continued)
Distance and Midpoints
Midpoint of a Segment
Midpoint on a
Number Line
If the coordinates of the endpoints of a segment are 𝑥1 and 𝑥2 ,
𝑥 +𝑥
then the coordinate of the midpoint of the segment is 1 2 2 .
Midpoint on a
Coordinate Plane
If a segment has endpoints with coordinates (𝑥1 , 𝑦1 ) and (𝑥2 , 𝑦2 ),
𝑥 +𝑥 𝑦 +𝑦
then the coordinates of the midpoint of the segment are ( 1 2 , 1 2 ).
2
2
Example 1: Find the coordinate of the midpoint of ̅̅̅̅
𝑷𝑸 .
The coordinates of P and Q are –3 and 1.
̅̅̅̅ , then the coordinate of M is −3 + 1 = −2 or –1.
If M is the midpoint of 𝑃𝑄
2
2
̅̅̅̅ , for P(–2, 4) and Q(4, 1).
Example 2: Find the coordinates of M, the midpoint of 𝑷𝑸
𝑥1 + 𝑥2 𝑦1 + 𝑦2
, 2 )
2
M=(
−2 + 4 4 + 1
, 2 )
2
=(
or (1, 2.5)
Exercises
Use the number line to find the coordinate of the
midpoint of each segment.
1. ̅̅̅̅
𝐶𝐸 –1
2. ̅̅̅̅
𝐷𝐺
4
̅̅̅̅ –3
3. 𝐴𝐹
4. ̅̅̅̅
𝐸𝐺
5
̅̅̅̅ –8
5. 𝐴𝐵
̅̅̅̅ –3 𝟏
7. 𝐵𝐷
̅̅̅̅
6. 𝐵𝐺
𝟏
̅̅̅̅
8. 𝐷𝐸
𝟐
𝟐
1
Find the coordinates of the midpoint of a segment with the given endpoints.
9. A(0, 0), B(12, 8)
(6, 4)
11. M(11, –2), N(–9, 13)
(1, 5.5)
13. S(10, –22), T(9, 10) (9.5, –6)
Chapter 1
10. R(–12, 8), S(6, 12)
(–3, 10)
12. E(–2, 6), F(–9, 3)
(–5.5, 4.5)
14. K(–11, 2), L(–19, 6) (–15, 4)
19
Glencoe Geometry