Find the Distance Between Two Points (-4,5) and (7,18)

$(- 4, 5)$ and $(7, 18)$

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.

$\sqrt{{(7 - (- 4))}^{2} + {(18 - 5)}^{2}}$

Step 3

Simplify.

Multiply $- 1$ by $- 4$ .

$\sqrt{{(7 + 4)}^{2} + {(18 - 5)}^{2}}$

Add $7$ and $4$ .

$\sqrt{11^{2} + {(18 - 5)}^{2}}$

Raise $11$ to the power of $2$ .

$\sqrt{121 + {(18 - 5)}^{2}}$

Subtract $5$ from $18$ .

$\sqrt{121 + 13^{2}}$

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

$\sqrt{121 + 169}$

Add $121$ and $169$ .

$\sqrt{290}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\sqrt{290}$

Decimal Form:

$17.02938636 \dots$

Step 5