# Distance Formula

Distance Formula, as evident from its name, is used to measure the shortest (straight-line) distance between two points.

### Pythagorean Theorem

A simple derivation of the formula can be obtained by applying this famous theorm.According to this theorem, the hypotenuse of a right-angled triangle can be obtained by

h^2 = x^2 + y^2

In the case of distance formula, we can measure the value of x by subtracting x1 from x2. Similarly, the value of y is given by y2-y1 as shown in the figure below. Eventually, the straight line distance d between the two points (x_1 , y_1) and (x_2 , y_2) is given by

d=sqrt((x_2- x_1)^2+ (y_2- y_1)^2 )

## Find the distance between the points (-1, 4) and (3, 6).

### 4.47 approx.

#### Explanation:

According to the Distance Formula, the distance between two points is given by

d=sqrt((x_2 - x_1)^2+ (y_2 - y_1)^2 )

Using the given coordinates as x_1 = -1, y_1 = 4, x_2 = 3, y_2 = 6;

d=sqrt((3-(-1))^2+ (6-4)^2 )

=>  d= sqrt((4)^2+ (2)^2 )

=>  d= sqrt20~~4.47

Therefore, the distance between the two given points is approximately 4.47

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

### 5.83 approx.

#### Explanation:

According to the Distance Formula, the distance between two points is given by

d=sqrt((x_2 - x_1)^2+ (y_2 - y_1)^2 )

Using the given coordinates as x_1 = 2, y_1 = -1, x_2 = -3, y_2 = 2;

d=sqrt((-3-2)^2+ (2-(-1))^2 )

=>  d= sqrt((-5)^2+ (3)^2 )

=>  d= sqrt34 ~~ 5.83

Therefore, the distance between the two given points is approximately 5.83

## WorkSheets

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