Download Midpoint and Distance Formulas

Geometry
Midpoint and Distance Formulas
Name ______________________________
Date ________________ Period ______
Objectives
Find the length and midpoint of a segment on a number line.
Develop and apply the formulas for distance midpoint on a coordinate plane.
Example 1
Find the length of each segment to the nearest millimeter.
X
Y
On the number line, the distance between any two points is the absolute value of the difference of the
coordinates. If the coordinates of points A and B are a and b, then the distance between A and B is
𝐴𝐵 = |a – b| or |b – a|
**NOTE**
Absolute Value
 The distance between two points.
 ABSOLUTE VALUE ALWAYS MAKES _______________ NUMBERS.
1. Inside Absolute Value, add or subtract or multiply or divide as normal.
2. When you bring the number out of Absolute Value, make it a positive number.
Midpoint is the point that divides the segment into two ________ length segments.
̅̅̅̅ , then AM = MB.
If M is the midpoint of 𝐴𝐵
Draw the picture and label it.
So if AB = 6, then AM = __ and MB = ___.
Example 2
Find the length of each segment then find its midpoint.
a. BC
b. AB
c. AC
Midpoint Formula In the Coordinate Plane
Example 3
Find the coordinates of the midpoint of ⃡𝑃𝑄 with
endpoints P(–8, 3) and Q(–2, 7).
Example 4
Find the coordinates of the midpoint of ⃡𝐸𝐹 with
endpoints E(–2, 3) and F(5, –3).
Example 5
M is the midpoint of XY. X has coordinates (2, 7) and
M has coordinates (6, 1). Find the coordinates of Y.
Example 6
S is the midpoint of RT. R has coordinates (–6, –1),
and S has coordinates (–1, 1). Find the coordinates of T.
Distance Formula In the Coordinate Plane
Example 7
Find FG and JK.
Example 8
Given E(–2, 1), F(–5, 5), G(–1, –2), H(3, 1).
Find EF and GH.
Example 9
The coordinates of the vertices of ∆ABC are A(2, 5), B(6, –1), and C(–4, –2).
Find the perimeter of ∆ABC, to the nearest tenth.