How to Find Distance of Two Points

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The distance between any \(2\) points is the length of the line segment which joins the points. There’s only a single line which passes through \(2\) points. Therefore, the distance between \(2\) points can be determined via locating the length of the line segment joining the \(2\) two points. For instance, if \(A\) and \(B\) are \(2\) points and if \(AB \ = \ 10 \ cm\), it signifies the distance between \(A\) and \(B\) is \(10 \ cm\).

Formula to Determine Distance Between Two Points:

The formula used for the distance, \(d\), between \(2\) points whose coordinates are \((x_{1},y_{1})\) and \((x_{2},y_{2})\) is:

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

That is known as the Distance Formula.

How do you Locate the Distance Between 2 Points?

The distance between \(2\) points utilizing the provided coordinates can be determined via the assistance of these steps:

Jot down the coordinates of the \(2\) given points in the coordinate plane as, \(A(x_{1},y_{1})\) and \(B(x_{2},y_{2})\).
You can use the distance formula to determine the distance between the \(2\) points: \(d = \sqrt{(x_1 \ -\ x_2)^2 \ +\ (y_1 \ -\ y_2)^2}\)
Show the answer in units.

Free printable Worksheets

Exercises for Finding Distance of Two Points

1) Find the distance between these points: \((0,6), (2,-6)\)\( \ \Rightarrow \ \)

2) Find the distance between these points: \((-4,8), (-2,-8)\)\( \ \Rightarrow \ \)

3) Find the distance between these points: \((-9,4), (6,-4)\)\( \ \Rightarrow \ \)

4) Find the distance between these points: \((5,5), (-5,-2)\)\( \ \Rightarrow \ \)

5) Find the distance between these points: \((0,-1), (-2,1)\)\( \ \Rightarrow \ \)

6) Find the distance between these points: \((-3,2), (1,-2)\)\( \ \Rightarrow \ \)

7) Find the distance between these points: \((7,3), (-3,-3)\)\( \ \Rightarrow \ \)

8) Find the distance between these points: \((-6,2), (4,-2)\)\( \ \Rightarrow \ \)

9) Find the distance between these points: \((7,-5), (-7,-2)\)\( \ \Rightarrow \ \)

10) Find the distance between these points: \((1,-3), (-4,3)\)\( \ \Rightarrow \ \)

Answers

1) Find the distance between these points: \((0,6), (2,-6)\)\( \ \Rightarrow \ \color{red}{D = \sqrt{(0 \ + \ 2)^2 + (6 \ + \ (-6))^2}} \)\( \ \Rightarrow \ \color{red}{D = \sqrt{4 + 0}} \)\( \ \Rightarrow \ \color{red}{D = 2}\)

2) Find the distance between these points: \((-4,8), (-2,-8)\)\( \ \Rightarrow \ \color{red}{D = \sqrt{(-4 \ + \ (-2))^2 + (8 \ + \ (-8))^2}} \)\( \ \Rightarrow \ \color{red}{D = \sqrt{36 + 0}} \)\( \ \Rightarrow \ \color{red}{D = 6}\)

3) Find the distance between these points: \((-9,4), (6,-4)\)\( \ \Rightarrow \ \color{red}{D = \sqrt{(-9 \ + \ 6)^2 + (4 \ + \ (-4))^2}} \)\( \ \Rightarrow \ \color{red}{D = \sqrt{9 + 0}} \)\( \ \Rightarrow \ \color{red}{D = 3}\)

4) Find the distance between these points: \((5,5), (-5,-2)\)\( \ \Rightarrow \ \color{red}{D = \sqrt{(5 \ + \ (-5))^2 + (5 \ + \ (-2))^2}} \)\( \ \Rightarrow \ \color{red}{D = \sqrt{0 + 9}} \)\( \ \Rightarrow \ \color{red}{D = 3}\)

5) Find the distance between these points: \((0,-1), (-2,1)\)\( \ \Rightarrow \ \color{red}{D = \sqrt{(0 \ + \ (-2))^2 + (-1 \ + \ 1)^2}} \)\( \ \Rightarrow \ \color{red}{D = \sqrt{4 + 0}} \)\( \ \Rightarrow \ \color{red}{D = 2}\)

6) Find the distance between these points: \((-3,2), (1,-2)\)\( \ \Rightarrow \ \color{red}{D = \sqrt{(-3 \ + \ 1)^2 + (2 \ + \ (-2))^2}} \)\( \ \Rightarrow \ \color{red}{D = \sqrt{4 + 0}} \)\( \ \Rightarrow \ \color{red}{D = 2}\)

7) Find the distance between these points: \((7,3), (-3,-3)\)\( \ \Rightarrow \ \color{red}{D = \sqrt{(7 \ + \ (-3))^2 + (3 \ + \ (-3))^2}} \)\( \ \Rightarrow \ \color{red}{D = \sqrt{16 + 0}} \)\( \ \Rightarrow \ \color{red}{D = 4}\)

8) Find the distance between these points: \((-6,2), (4,-2)\)\( \ \Rightarrow \ \color{red}{D = \sqrt{(-6 \ + \ 4)^2 + (2 \ + \ (-2))^2}} \)\( \ \Rightarrow \ \color{red}{D = \sqrt{4 + 0}} \)\( \ \Rightarrow \ \color{red}{D = 2}\)

9) Find the distance between these points: \((7,-5), (-7,-2)\)\( \ \Rightarrow \ \color{red}{D = \sqrt{(7 \ + \ (-7))^2 + (-5 \ + \ (-2))^2}} \)\( \ \Rightarrow \ \color{red}{D = \sqrt{0 + 49}} \)\( \ \Rightarrow \ \color{red}{D = 7}\)

10) Find the distance between these points: \((1,-3), (-4,3)\)\( \ \Rightarrow \ \color{red}{D = \sqrt{(1 \ + \ (-4))^2 + (-3 \ + \ 3)^2}} \)\( \ \Rightarrow \ \color{red}{D = \sqrt{9 + 0}} \)\( \ \Rightarrow \ \color{red}{D = 3}\)

How to Find Distance of Two Points