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.

Distance and Midpoint Formulas

Chapter 11, Section 3

Finding DistanceUse 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 = √(x₂ – x₁)² + (y₂ – y₁)²X and Y are from coordinate points. ex.

(5, -2)

Find the Distance between A(6,3) and B(1,9)

D = √(x₂ – x₁)² + (y₂ – y₁)²It doesn't matter which coordinate is 1

or 2.Because a -#² = +#D = √(6₂ – 1₁)² + (9₂ – 3₁)²D = √(5)² + (6)²D = √(25 + 36)D = √(61)D ≈ 7.8 (rounded to tenth)

Use Distance FormulaD = √(x₂ – x₁)² + (y₂ – y₁)²

Distance 1: (3, 8), (2, 4)

Distance 2: (10, -3), (1, 0)

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.

Midpoint FormulaThe midpoint of a segment is the POINT M.The midpoint is a dot with a coordinate (x, y).

M = ( [x₁ + 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 )

Find the MidpointM = ( [x₁ + 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

Find the Midpoints

Midpoint between A(2, 5) and B(8, 1):

Midpoint between P(-4, -2) and Q(2, 3):

Assignment #32

Pages 575-576: 1-6 all, 8-21 all.