Midpoint and Midpoint and Distance FormulasDistance Formulas

Distance FormulaDistance Formula

(x2 x

1)2 (y

2 y

1)2

The distance formula is used to find the distance of a line segment.

Example 1: Find the distance between the points Example 1: Find the distance between the points (-5, -1) and (3, 5)in simplest radical form.(-5, -1) and (3, 5)in simplest radical form.

distance formula

fill in your x- and y-values

simplify by subtracting before squaring

square each value

add your squared values

remember the square root of 100 in simplest form is 10

(x2 x

1)2 (y

2 y

1)2

(3 ( 5))2 (5 ( 1))2

(8)2 (6)2

64 36

100

10

Example 2: A coordinate plane is superimposed on a map of Example 2: A coordinate plane is superimposed on a map of North Carolina. Greenville is located at (350, 75) and Charlotte is North Carolina. Greenville is located at (350, 75) and Charlotte is located at (120, 130). Find the straight-line distance between the located at (120, 130). Find the straight-line distance between the

two cities. two cities. Write your answer in decimal form.Write your answer in decimal form.

answer is 236.48answer is 236.48

(x2 x

1)2 (y

2 y

1)2

(120 350)2 (130 75)2

( 230)2 (55)2

52900 3025

55925

Midpoint FormulaMidpoint Formula

(x

1 x

2

2),(

y1 y

2

2)

The midpoint formula is used to find the middle of a line segment. You take the average of the x-values and take the average of the y-

values.

Example 4: On a map’s coordinate grid, Greenville is located (-4, 3) and Raleigh is Example 4: On a map’s coordinate grid, Greenville is located (-4, 3) and Raleigh is located at (6, 9). The distance from Greenville to Wilson is half the distance from located at (6, 9). The distance from Greenville to Wilson is half the distance from

Greenville to Raleigh. What is the approximate distance from Greenville to Wilson? Greenville to Raleigh. What is the approximate distance from Greenville to Wilson? Round your answer to the nearest hundredth.Round your answer to the nearest hundredth.

We know that from Greenville to Wilsonand from Wilson to Raleigh it is the same distance. So we know that Wilson is ourmidpoint.

Step 1 – Find the midpoint from Greenvilleto Raleigh (this will give us Wilson’s location on the map.

( 4 6

2,3 9

2)

(2

2,12

2) (1,6)

Step 2 – Now that we know thelocation of Wilson we can use it tofind the distance from it to Greenville.

(1 ( 4)2 (6 3)2

(5)2 (3)2

25 9

34Distance is about 5.830951894845…so if we round that to the nearest hundredth it is about 5.83 miles on the map.