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)

$(0,6), (2,-6)$

\Rightarrow D = \sqrt{(0 + 2)^{2} + (6 + (- 6))^{2}}

$\ \Rightarrow \ \color{red}{D = \sqrt{(0 \ + \ 2)^2 + (6 \ + \ (-6))^2}}$

\Rightarrow D = \sqrt{4 + 0}

$\ \Rightarrow \ \color{red}{D = \sqrt{4 + 0}}$

\Rightarrow D = 2

$\ \Rightarrow \ \color{red}{D = 2}$

2) Find the distance between these points:

(- 4, 8), (- 2, - 8)

$(-4,8), (-2,-8)$

\Rightarrow D = \sqrt{(- 4 + (- 2))^{2} + (8 + (- 8))^{2}}

$\ \Rightarrow \ \color{red}{D = \sqrt{(-4 \ + \ (-2))^2 + (8 \ + \ (-8))^2}}$

\Rightarrow D = \sqrt{36 + 0}

$\ \Rightarrow \ \color{red}{D = \sqrt{36 + 0}}$

\Rightarrow D = 6

$\ \Rightarrow \ \color{red}{D = 6}$

3) Find the distance between these points:

(- 9, 4), (6, - 4)

$(-9,4), (6,-4)$

\Rightarrow D = \sqrt{(- 9 + 6)^{2} + (4 + (- 4))^{2}}

$\ \Rightarrow \ \color{red}{D = \sqrt{(-9 \ + \ 6)^2 + (4 \ + \ (-4))^2}}$

\Rightarrow D = \sqrt{9 + 0}

$\ \Rightarrow \ \color{red}{D = \sqrt{9 + 0}}$

\Rightarrow D = 3

$\ \Rightarrow \ \color{red}{D = 3}$

4) Find the distance between these points:

(5, 5), (- 5, - 2)

$(5,5), (-5,-2)$

\Rightarrow D = \sqrt{(5 + (- 5))^{2} + (5 + (- 2))^{2}}

$\ \Rightarrow \ \color{red}{D = \sqrt{(5 \ + \ (-5))^2 + (5 \ + \ (-2))^2}}$

\Rightarrow D = \sqrt{0 + 9}

$\ \Rightarrow \ \color{red}{D = \sqrt{0 + 9}}$

\Rightarrow D = 3

$\ \Rightarrow \ \color{red}{D = 3}$

5) Find the distance between these points:

(0, - 1), (- 2, 1)

$(0,-1), (-2,1)$

\Rightarrow D = \sqrt{(0 + (- 2))^{2} + (- 1 + 1)^{2}}

$\ \Rightarrow \ \color{red}{D = \sqrt{(0 \ + \ (-2))^2 + (-1 \ + \ 1)^2}}$

\Rightarrow D = \sqrt{4 + 0}

$\ \Rightarrow \ \color{red}{D = \sqrt{4 + 0}}$

\Rightarrow D = 2

$\ \Rightarrow \ \color{red}{D = 2}$

6) Find the distance between these points:

(- 3, 2), (1, - 2)

$(-3,2), (1,-2)$

\Rightarrow D = \sqrt{(- 3 + 1)^{2} + (2 + (- 2))^{2}}

$\ \Rightarrow \ \color{red}{D = \sqrt{(-3 \ + \ 1)^2 + (2 \ + \ (-2))^2}}$

\Rightarrow D = \sqrt{4 + 0}

$\ \Rightarrow \ \color{red}{D = \sqrt{4 + 0}}$

\Rightarrow D = 2

$\ \Rightarrow \ \color{red}{D = 2}$

7) Find the distance between these points:

(7, 3), (- 3, - 3)

$(7,3), (-3,-3)$

\Rightarrow D = \sqrt{(7 + (- 3))^{2} + (3 + (- 3))^{2}}

$\ \Rightarrow \ \color{red}{D = \sqrt{(7 \ + \ (-3))^2 + (3 \ + \ (-3))^2}}$

\Rightarrow D = \sqrt{16 + 0}

$\ \Rightarrow \ \color{red}{D = \sqrt{16 + 0}}$

\Rightarrow D = 4

$\ \Rightarrow \ \color{red}{D = 4}$

8) Find the distance between these points:

(- 6, 2), (4, - 2)

$(-6,2), (4,-2)$

\Rightarrow D = \sqrt{(- 6 + 4)^{2} + (2 + (- 2))^{2}}

$\ \Rightarrow \ \color{red}{D = \sqrt{(-6 \ + \ 4)^2 + (2 \ + \ (-2))^2}}$

\Rightarrow D = \sqrt{4 + 0}

$\ \Rightarrow \ \color{red}{D = \sqrt{4 + 0}}$

\Rightarrow D = 2

$\ \Rightarrow \ \color{red}{D = 2}$

9) Find the distance between these points:

(7, - 5), (- 7, - 2)

$(7,-5), (-7,-2)$

\Rightarrow D = \sqrt{(7 + (- 7))^{2} + (- 5 + (- 2))^{2}}

$\ \Rightarrow \ \color{red}{D = \sqrt{(7 \ + \ (-7))^2 + (-5 \ + \ (-2))^2}}$

\Rightarrow D = \sqrt{0 + 49}

$\ \Rightarrow \ \color{red}{D = \sqrt{0 + 49}}$

\Rightarrow D = 7

$\ \Rightarrow \ \color{red}{D = 7}$

10) Find the distance between these points:

(1, - 3), (- 4, 3)

$(1,-3), (-4,3)$

\Rightarrow D = \sqrt{(1 + (- 4))^{2} + (- 3 + 3)^{2}}

$\ \Rightarrow \ \color{red}{D = \sqrt{(1 \ + \ (-4))^2 + (-3 \ + \ 3)^2}}$

\Rightarrow D = \sqrt{9 + 0}

$\ \Rightarrow \ \color{red}{D = \sqrt{9 + 0}}$

\Rightarrow D = 3

$\ \Rightarrow \ \color{red}{D = 3}$

How to Find Distance of Two Points