Find the Distance Between Two Points (3,-6) , (8,10)

$(3, - 6)$ , $(8, 10)$

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.

$\sqrt{{(8 - 3)}^{2} + {(10 - (- 6))}^{2}}$

Step 3

Simplify.

Subtract $3$ from $8$ .

$\sqrt{5^{2} + {(10 - (- 6))}^{2}}$

Raise $5$ to the power of $2$ .

$\sqrt{25 + {(10 - (- 6))}^{2}}$

Multiply $- 1$ by $- 6$ .

$\sqrt{25 + {(10 + 6)}^{2}}$

Add $10$ and $6$ .

$\sqrt{25 + 16^{2}}$

Raise $16$ to the power of $2$ .

$\sqrt{25 + 256}$

Add $25$ and $256$ .

$\sqrt{281}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\sqrt{281}$

Decimal Form:

$16.76305461 \dots$

Step 5