Solving Distance Formula

Introduction to solving distance formula:
Distance formula is a formula which is used to find the distance between two points (x1, y1) and (x2, y2). This formula is based on the Pythagorean Theorem.Solving problems using distance formula is one of the easier method to find the distance between two given points.

The distance d between the points (x1, y1) and (x 2, y2) is given as,

d = v ((x2 - x1)2 + (y2 - y1)2)

Example Problems on Solving Distances Using Distance Formula:


1) Find the distance between the points (-2, -3) and (-4, 4).

Solution:

Let (x1, y1) = (-2, -3)

(x2, y2) = (-4, 4)

By distance formula, d = v ((x2 - x1)2 + (y2 - y1)2)

=  v (((-4 - (-2))2 + (4 - (-3))2)

=  v ((-2)2  + (7)2)

=  v (4 + 49)

= v53

Solving for d, we get d  ˜ 7.28

2) Find the distance between the points (2, 4) and (5, -1).

Solution:

Let (x1, y1) = (2, 4)

(x2, y2) = (5, -1)

By distance formula, d = v ((x2 - x1)2 + (y2 - y1)2)

=  v ((5 - 2)2 + (-1-4)2)

=  v (32 + (-5)2)

=  v (9 + 25)

= v 34

Solving for d, we get d ˜ 5.83

3) Find the distance between the points (-2, 1) and (1, 5).

Solution:

Let (x1, y1) = (-2, 1)

(x2, y2) = (1, 5)

By distance formula, d = v ((x2 - x1)2 + (y2 - y1)2)

=  v ((1 - (-2))2 + (5 - 1)2

=  v (32 + 42)

=  v (9 + 16)

d  = v 25

Solving for d, we get   d = 5

4) If the distance from the point is (1, 2) to the point (3,y) is v8.  Find the value of  y.

Solution:

Let (x1, y1) = (1, 2)

(x2, y2) = (3, y)

d = v8

By distance formula, d = v ((x2 - x1)2 + (y2 - y1)2)

v8 = v ((3 - 1)2 + (y - 2)2

8 = 22 + (y - 2)2

8 = 4 + (y - 2)2

8 - 4 = (y 2 - 4y + 4)

4 = y 2 - 4y + 4

0 =  y 2 - 4y

0 = y (y - 4)

Solving for y. we get

y = 0 ;   y = 4
   


Solve the Problems Using Distance Formula:

Find the distance between the following points,

(1, 4) and (4, 0)

(2, 8) and  (16, 4)

(8, 5) and (9, 6)

(5, 6) and (-12, 40)

Solutions:

d = 5
d = 14.56
d = 1.41
d = 38.01