Midpoint Formula, & Distance Formula Warm Up Simplify. 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

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| AB = |a – b| or |b - a| A a B b **NOTE** Absolute Value The distance between two points. ABSOLUTE VALUE ALWAYS MAKES POSITIVE NUMBERS. Inside Absolute Value, add or subtract or multiply or divide as normal. 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 𝐴𝐵 , then AM = MB. So if AB = 6, then AM = __ and MB = ___. Draw the picture and label it.

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).

Warm Up 8-15-14 Graph the segment CD with endpoints C(0,-2) and D(4,5) 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 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.

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.