Find the Distance Between Two Points (8,-3) and (4,6)

$(8, - 3)$ and $(4, 6)$

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.

$\sqrt{{(4 - 8)}^{2} + {(6 - (- 3))}^{2}}$

Step 3

Simplify.

Subtract $8$ from $4$ .

$\sqrt{{(- 4)}^{2} + {(6 - (- 3))}^{2}}$

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

$\sqrt{16 + {(6 - (- 3))}^{2}}$

Multiply $- 1$ by $- 3$ .

$\sqrt{16 + {(6 + 3)}^{2}}$

Add $6$ and $3$ .

$\sqrt{16 + 9^{2}}$

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

$\sqrt{16 + 81}$

Add $16$ and $81$ .

$\sqrt{97}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\sqrt{97}$

Decimal Form:

$9.84885780 \dots$

Step 5