# Distance Between 2 Points

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Distance between 2 points can be found by using distance formula. The distance is the amount of space between points, lines etc.  In mathematics the distance formula is an expression used to determine the distance between two points in a plane.  The distance between two points with coordinates (x1, y1) and (x2, y2) can be represented by a formula

Distance = √ ((x2- x1) ^2 + (y2 – y1) ^2)

The distance formula is obtained from Pythagorean Theorem.

The below two examples illustrate how to find out distance between two points.

Problem 1: Calculate the distance between the two points P (2, 1) and Q (−3, 2).

Solution: According to the question the coordinates of two points are P (2, 1) and Q (-3, 2).

=> To find out distance between P and Q use distance formula

=> Distance = √ ((x2- x1) ^2 + (y2 – y1) ^2)

= √ ((-3- 2) ^2 + (2 – 1) ^2) = √ ((-5) ^2 + (1) ^2) = Distance = √ 26

=> The distance between PQ = Distance = √ 26

Problem 2: The distance between the points A (-2, -3) and B (-3, x) is equal to 5. Find value of x.

Solution: Given the distance between two points is 5

=> Since the distance is known we can use distance formula to set up an equation

=> Distance = √ ((x2- x1) ^2 + (y2 – y1) ^2)

=> 5 = √ ((-3 – (-2)) ^2 + (x – (-3)) ^2)

=> 5 = √ ((-1) ^2 + (x + 3) ^2)

=> 5^2 = 1 + (x + 3) ^2

=> (x + 3) ^2 = 24

=> We get 2 solutions for x

=> -3 – 2 sqrt (6) and -3+ 2 sqrt (6).