Find the Distance Between Two Points (5,1) , (9,-6)

$(5, 1)$ , $(9, - 6)$

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.

$\sqrt{{(9 - 5)}^{2} + {((- 6) - 1)}^{2}}$

Step 3

Simplify.

Subtract $5$ from $9$ .

$\sqrt{4^{2} + {((- 6) - 1)}^{2}}$

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

$\sqrt{16 + {((- 6) - 1)}^{2}}$

Subtract $1$ from $- 6$ .

$\sqrt{16 + {(- 7)}^{2}}$

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