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

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

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.

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

Step 3

Simplify.

Subtract $3$ from $5$ .

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

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

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

Multiply $- 1$ by $- 4$ .

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

Add $4$ and $4$ .

$\sqrt{4 + 8^{2}}$

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

$\sqrt{4 + 64}$

Add $4$ and $64$ .

$\sqrt{68}$

Rewrite $68$ as $2^{2} \cdot 17$ .

Factor $4$ out of $68$ .

$\sqrt{4 (17)}$

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

$\sqrt{2^{2} \cdot 17}$

Pull terms out from under the radical.

$2 \sqrt{17}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$2 \sqrt{17}$

Decimal Form:

$8.24621125 \dots$

Step 5