Find the Distance Between Two Points (5,7) , (-3,4)

$(5, 7)$ , $(- 3, 4)$

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.

$\sqrt{{((- 3) - 5)}^{2} + {(4 - 7)}^{2}}$

Step 3

Simplify.

Subtract $5$ from $- 3$ .

$\sqrt{{(- 8)}^{2} + {(4 - 7)}^{2}}$

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

$\sqrt{64 + {(4 - 7)}^{2}}$

Subtract $7$ from $4$ .

$\sqrt{64 + {(- 3)}^{2}}$

Raise $- 3$ to the power of $2$ .

$\sqrt{64 + 9}$

Add $64$ and $9$ .

$\sqrt{73}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\sqrt{73}$

Decimal Form:

$8.54400374 \dots$

Step 5