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

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

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.

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

Step 3

Simplify.

Subtract $5$ from $- 4$ .

$\sqrt{{(- 9)}^{2} + {(3 - 7)}^{2}}$

Raise $- 9$ to the power of $2$ .

$\sqrt{81 + {(3 - 7)}^{2}}$

Subtract $7$ from $3$ .

$\sqrt{81 + {(- 4)}^{2}}$

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

$\sqrt{81 + 16}$

Add $81$ and $16$ .

$\sqrt{97}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\sqrt{97}$

Decimal Form:

$9.84885780 \dots$

Step 5