Find the Distance Between Two Points (5,8) , (-3,4)

$(5, 8)$ , $(- 3, 4)$

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.

$\sqrt{{((- 3) - 5)}^{2} + {(4 - 8)}^{2}}$

Step 3

Simplify.

Subtract $5$ from $- 3$ .

$\sqrt{{(- 8)}^{2} + {(4 - 8)}^{2}}$

Raise $- 8$ to the power of $2$ .

$\sqrt{64 + {(4 - 8)}^{2}}$

Subtract $8$ from $4$ .

$\sqrt{64 + {(- 4)}^{2}}$

Raise $- 4$ to the power of $2$ .

$\sqrt{64 + 16}$

Add $64$ and $16$ .

$\sqrt{80}$

Rewrite $80$ as $4^{2} \cdot 5$ .

Factor $16$ out of $80$ .

$\sqrt{16 (5)}$

Rewrite $16$ as $4^{2}$ .

$\sqrt{4^{2} \cdot 5}$

Pull terms out from under the radical.

$4 \sqrt{5}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$4 \sqrt{5}$

Decimal Form:

$8.94427190 \dots$

Step 5