Find the Distance Between Two Points (0,-10) , (1,-3)

$(0, - 10)$ , $(1, - 3)$

Step 1

Use the distance formula to determine the distance between the two points.

$Distance = \sqrt{{(x_{2} - x_{1})}^{2} + {(y_{2} - y_{1})}^{2}}$

Step 2

Substitute the actual values of the points into the distance formula.

$\sqrt{{(1 - 0)}^{2} + {((- 3) - (- 10))}^{2}}$

Step 3

Simplify.

Subtract $0$ from $1$ .

$\sqrt{1^{2} + {((- 3) - (- 10))}^{2}}$

One to any power is one.

$\sqrt{1 + {((- 3) - (- 10))}^{2}}$

Multiply $- 1$ by $- 10$ .

$\sqrt{1 + {(- 3 + 10)}^{2}}$

Add $- 3$ and $10$ .

$\sqrt{1 + 7^{2}}$

Raise $7$ to the power of $2$ .

$\sqrt{1 + 49}$

Add $1$ and $49$ .

$\sqrt{50}$

Rewrite $50$ as $5^{2} \cdot 2$ .

Factor $25$ out of $50$ .

$\sqrt{25 (2)}$

Rewrite $25$ as $5^{2}$ .

$\sqrt{5^{2} \cdot 2}$

Pull terms out from under the radical.

$5 \sqrt{2}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$5 \sqrt{2}$

Decimal Form:

$7.07106781 \dots$

Step 5