Midpoint Formula, & Distance Formula

Warm UpSimplify.1. 7 – (–3) 2. –1 – (–13) 3. |7 – 1|

4. Graph A (–2, 3) and B (1, 0). 5. Simplify.

Distance Formula, & Midpoint Formula

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

AB = |a – b| or |b - a|A

a

B

b

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 = |a – b| or |b – a|

**NOTE** Absolute Value The distance between two points. ABSOLUTE VALUE ALWAYS MAKES POSITIVE 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.

If M is the midpoint of , then AM = MB.

So if AB = 6, then AM = __ and MB = ___.Draw the picture and label it.

Example 2Find the length of each segment then find its midpoint.

a. BC b. AB c. AC

Midpoint Formula In the Coordinate Plane

Example 3Find the coordinates of the midpoint of with endpoints P(–8, 3) and Q(–2, 7).

Example 4Find the coordinates of the midpoint of with endpoints E(–2, 3) and F(5, –3).

Warm Up 8-15-14

Graph the segment CD with endpoints C(0,-2) and D(4,5).

Use the midpoint formula to find the midpoint M of CD.

Example 5M is the midpoint of XY. X has coordinates (2, 7) and M has coordinates (6, 1). Find the coordinates of Y.

Example 6S is the midpoint of RT. R has coordinates (–6, –1), and S has coordinates (–1, 1). Find the coordinates of T.

Example 7Find FG and JK.

Example 8Given E(–2, 1), F(–5, 5), G(–1, –2), H(3, 1).Find EF and GH.

Example 9The 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.