Lesson 19:The Distance Formula

Thedistance formulastates that the distancedbetween any two points with coordinates (x1, y1) and (x2, y2) is given by the following equation:d = SQRT[(x2- x1)2+ (y2- y1)2]. Note: SQRT means "square root"

So, substitute the x and y values with the coordinate values. then calculate according to the formula. Finally, calculate the square root of the final answer.

Example

1. Problem: Find the distance between

(-2, 3) and (8, -1).

Solution:Plug any given information into the distance equation.

d= SQRT[ (8 - (-2))²+ (-1 - 3)²]

Simplify.

d= SQRT[10²+ (-4)²]

d= SQRT(100 + 16)

d= 2(SQRT(29))

The Midpoint formula is a little easier.

To find the coordinates of any midpoint of a line segment with given end points, simply follow these steps;

calculate the sum of the two x values and divide by 2

calculate the sum of the two y values and divide by 2

Example:

Calculating the values willgive you the midpoint coordinates

For the following coordinate pairs, calculate the midpoint value;

Lesson 3 Review:

1. Find the distance and the midpoints between each of the following given pairs of points.

a) (0, 5) and (0 -6)

b) (3, 0) and (-4, 0)

c) (5, 2) and (7, 6)

d) (-3, 4) and (1, -3)

e) (6, 4) and (2, 1)

f) (-2, -4) and (3, 8)

g) (0, 0) and (5, 10)

h) (2, 1) and (4, 0)

i) (6, 4) and (6, -2) j) (-5, 2) and (7, -7)