Find the Distance Between Two Points (9,-4) and (5,3)

$(9, - 4)$ and $(5, 3)$

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.

$\sqrt{{(5 - 9)}^{2} + {(3 - (- 4))}^{2}}$

Step 3

Simplify.

Subtract $9$ from $5$ .

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

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

$\sqrt{16 + {(3 - (- 4))}^{2}}$

Multiply $- 1$ by $- 4$ .

$\sqrt{16 + {(3 + 4)}^{2}}$

Add $3$ and $4$ .

$\sqrt{16 + 7^{2}}$

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

$\sqrt{16 + 49}$

Add $16$ and $49$ .

$\sqrt{65}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\sqrt{65}$

Decimal Form:

$8.06225774 \dots$

Step 5