Find the Distance Between Two Points (-4,6) and (3,-7)

$(- 4, 6)$ and $(3, - 7)$

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.

$\sqrt{{(3 - (- 4))}^{2} + {((- 7) - 6)}^{2}}$

Step 3

Simplify.

Multiply $- 1$ by $- 4$ .

$\sqrt{{(3 + 4)}^{2} + {((- 7) - 6)}^{2}}$

Add $3$ and $4$ .

$\sqrt{7^{2} + {((- 7) - 6)}^{2}}$

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

$\sqrt{49 + {((- 7) - 6)}^{2}}$

Subtract $6$ from $- 7$ .

$\sqrt{49 + {(- 13)}^{2}}$

Raise $- 13$ to the power of $2$ .

$\sqrt{49 + 169}$

Add $49$ and $169$ .

$\sqrt{218}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\sqrt{218}$

Decimal Form:

$14.76482306 \dots$

Step 5