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

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

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.

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

Step 3

Simplify.

Subtract $1$ from $5$ .

$\sqrt{4^{2} + {(6 - (- 9))}^{2}}$

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

$\sqrt{16 + {(6 - (- 9))}^{2}}$

Multiply $- 1$ by $- 9$ .

$\sqrt{16 + {(6 + 9)}^{2}}$

Add $6$ and $9$ .

$\sqrt{16 + 15^{2}}$

Raise $15$ to the power of $2$ .

$\sqrt{16 + 225}$

Add $16$ and $225$ .

$\sqrt{241}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\sqrt{241}$

Decimal Form:

$15.52417469 \dots$

Step 5