Find the Distance Between Two Points Find the distance between (-12,1) and (12,-1)

Find the distance between $(- 12, 1)$ and $(12, - 1)$

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.

$\sqrt{{(12 - (- 12))}^{2} + {((- 1) - 1)}^{2}}$

Step 3

Simplify.

Multiply $- 1$ by $- 12$ .

$\sqrt{{(12 + 12)}^{2} + {((- 1) - 1)}^{2}}$

Add $12$ and $12$ .

$\sqrt{24^{2} + {((- 1) - 1)}^{2}}$

Raise $24$ to the power of $2$ .

$\sqrt{576 + {((- 1) - 1)}^{2}}$

Subtract $1$ from $- 1$ .

$\sqrt{576 + {(- 2)}^{2}}$

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

$\sqrt{576 + 4}$

Add $576$ and $4$ .

$\sqrt{580}$

Rewrite $580$ as $2^{2} \cdot 145$ .

Factor $4$ out of $580$ .

$\sqrt{4 (145)}$

Rewrite $4$ as $2^{2}$ .

$\sqrt{2^{2} \cdot 145}$

Pull terms out from under the radical.

$2 \sqrt{145}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$2 \sqrt{145}$

Decimal Form:

$24.08318915 \dots$

Step 5