# How to Find Distance of Two Points? (+FREE Worksheet!)

Learn how to find the distance of two points on the coordinate plane by using the distance formula. ## Step by step guide to find the distance of two points

• Distance of two points A $$(x_{1},y_{1})$$ and B $$(x_{2},y_{2})$$
$$\color{blue}{d=\sqrt{(x_2-x_1)^{2}+(y_{2}-y_{1}){^2}}}$$

### Finding Distance of Two Points – Example 1:

Find the distance of two points $$(1,6)$$ and $$(4,2)$$.

Solution:

Use distance of two points formula: $$\color{blue}{d=\sqrt{(x_2-x_1)^{2}+(y_{2}-y_{1}){^2}}}$$
$$(x_{1},y_{1})=(1,6)$$ and $$(x_{2},y_{2})=(4,2)$$. Then: →
$$d=\sqrt{(4−1)^{2}+(2−6)^{2}}=\sqrt{(3)^{2}+(−4)^{2}}=\sqrt{9+16}=\sqrt{25}=5→d=5$$

### Finding Distance of Two Points – Example 2:

Find the distance of two points $$(-1,5)$$ and $$(-3,-6)$$.

Solution:

Use distance of two points formula: $$\color{blue}{d=\sqrt{(x_2-x_1)^{2}+(y_{2}-y_{1}){^2}}}$$
$$(x_{1},y_{1})=(-1,5)$$ and $$(x_{2},y_{2})=(-3,-6)$$. Then: $$→$$
$$d=\sqrt{(-3−(-1))^{2}+(-6−5)^{2}}=\sqrt{(-2)^{2}+(−11)^{2}}=\sqrt{4+121}=\sqrt{125}=5\sqrt{5}$$ → $$d=5 \sqrt{5}$$

### Finding Distance of Two Points – Example 3:

Find the distance of two points $$(0,8)$$ and $$(-4,5)$$.

Solution:

Use distance of two points formula: $$\color{blue}{d=\sqrt{(x_2-x_1)^{2}+(y_{2}-y_{1}){^2}}}$$
$$(x_{1},y_{1})=(0,8)$$ and $$(x_{2},y_{2})=(−4,5)$$. Then:→
$$d=\sqrt{(−4−0)^2+(5−8)^2}=\sqrt{(-4)^2+(-3)^2}=\sqrt{16+9}=\sqrt{25}=5→d=5$$

### Finding Distance of Two Points – Example 4:

Find the distance of two points $$(4,2)$$ and $$(-5,-10)$$.

Solution:

Use distance of two points formula: $$\color{blue}{d=\sqrt{(x_2-x_1)^{2}+(y_{2}-y_{1}){^2}}}$$
$$(x_{1},y_{1})=(4,2)$$ and $$(x_{2},y_{2})=(−5,-10)$$. Then: →
$$d=\sqrt{( − 5−4)^2+(−10-2)^2}=\sqrt{(-9)^2+(-12)^2}=\sqrt{81+144}=\sqrt{225}=15→d=15$$

## Exercises for Finding Distance of Two Points

### Find the distance between each pair of points.

1. $$\color{blue}{(2, –1), ( 1, – 1)}$$
2. $$\color{blue}{ (6, 4), (– 2, 10)}$$
3. $$\color{blue}{(– 8, – 5), (– 5, -1)}$$
4. $$\color{blue}{(– 6, – 10), (– 2, – 10)}$$
5. $$\color{blue}{(4, – 6), (9, 6)}$$
6. $$\color{blue}{(– 6, – 7), (2, 8)}$$

1. $$\color{blue}{1}$$
2. $$\color{blue}{10}$$
3. $$\color{blue}{5}$$
4. $$\color{blue}{4}$$
5. $$\color{blue}{13}$$
6. $$\color{blue}{17}$$

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