This document provides instructions and examples for using the distance and midpoint formulas in coordinate geometry. It explains that the distance formula, which uses Pythagorean theorem, can find the length of a segment on a coordinate plane between two points. The midpoint formula is also explained, which finds the midpoint of a segment by taking the average of the x- and y-coordinates of the two points. Several examples are worked out finding distances and midpoints between points on a coordinate plane.

1. Warm Up: Find the missing length to the nearest tenth of a unit. Both triangles are right triangles. Triangle 1: Legs: 8ft and 12ft; find Hypotenuse. Triangle 2: Leg: 10mm, Hypotenuse: 25mm; find Leg.

2. Distance and Midpoint Formulas Chapter 11, Section 3

3. Finding Distance Use Pythagorean Theorem to find the length of a segment on a coordinate plane. Make a Right Triangle to do this. Or, just use the Distance Formula that is based off of Pythagorean's Theorem. Distance = √ (x ₂ – x ₁ ) ² + (y ₂ – y ₁ ) ² X and Y are from coordinate points. ex. (5, -2)

4. Find the Distance between A( 6 , 3 ) and B( 1 , 9 ) D = √ ( x ₂ – x ₁ ) ² + ( y ₂ – y ₁ ) ² It doesn't matter which coordinate is 1 or 2. Because a -#² = +# D = √ ( 6 ₂ – 1 ₁ ) ² + ( 9 ₂ – 3 ₁ ) ² D = √ ( 5 ) ² + ( 6 ) ² D = √ ( 25 + 36 ) D = √ (61) D ≈ 7.8 (rounded to tenth)

5. Use Distance Formula D = √ ( x ₂ – x ₁ ) ² + ( y ₂ – y ₁ ) ² Distance 1: ( 3 , 8 ), ( 2 , 4 ) Distance 2: ( 10 , -3 ), ( 1 , 0 )

6. Use Distance Formula to Determine Perimeter Find Distance between each point, then add them to find perimeter. AB = ? BC = ? CD = ? DA = ? D (3, 3) A (0, -1) B (8, 0) C (9, 4) √ 65 √ 17 √ 37 √ 25 = 5 These numbers add up to 23.2681259 units, which is the perimeter.

7. Midpoint Formula The midpoint of a segment is the POINT M. The midpoint is a dot with a coordinate (x, y). M = ( [x ₁ + x₂]/2 , [y₁ + y₂]/2 ) Take the x coordinates, add, divide by 2 = new x coordinate. Take the y coordinates, add, divide by 2 = new y coordinate. M = ( x , y )

8. Find the Midpoint M = ( [x ₁ + x₂]/2 , [y₁ + y₂]/2 ) Find the midpoint between: G( -3 , 2 ) and H( 7 , -2 ) ( [ -3 + 7 ]/2, [ 2 + -2 ]/2 ) ( [4]/2, [0]/2 ) ( 2, 0 ) ← Midpoint between G and H

9. Find the Midpoints Midpoint between A(2, 5) and B(8, 1): Midpoint between P(-4, -2) and Q(2, 3):

10. Assignment #32 Pages 575-576: 1-6 all, 8-21 all.