## How to Find Distance of Two Points

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

### 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 \$$

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: $$(1,-3), (-4,3)$$$$\ \Rightarrow \ \color{red}{D = \sqrt{(1 \ + \ (-4))^2 + (-3 \ + \ 3)^2}}$$$$\ \Rightarrow \ \color{red}{D = \sqrt{9 + 0}}$$$$\ \Rightarrow \ \color{red}{D = 3}$$

## Finding Distance of Two Points Quiz

### ALEKS Math Practice Workbook 2022

$26.99$12.99

### ParaPro Math in 10 Days

$17.99$12.99

### GED Math in 10 Days

$26.99$13.99

### CLEP College Math in 10 Days

$24.99$13.99