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.

Distance Formula

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 )`

Distance Formula Examples

Example 1:

 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


Example 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






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