Find the Distance Between Two Points (-5,4) , (1,-3)

$(- 5, 4)$ , $(1, - 3)$

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.

$\sqrt{{(1 - (- 5))}^{2} + {((- 3) - 4)}^{2}}$

Step 3

Simplify.

Multiply $- 1$ by $- 5$ .

$\sqrt{{(1 + 5)}^{2} + {((- 3) - 4)}^{2}}$

Add $1$ and $5$ .

$\sqrt{6^{2} + {((- 3) - 4)}^{2}}$

Raise $6$ to the power of $2$ .

$\sqrt{36 + {((- 3) - 4)}^{2}}$

Subtract $4$ from $- 3$ .

$\sqrt{36 + {(- 7)}^{2}}$

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

$\sqrt{36 + 49}$

Add $36$ and $49$ .

$\sqrt{85}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\sqrt{85}$

Decimal Form:

$9.21954445 \dots$

Step 5