Find the Distance Between Two Points (2,-3) and (-4,-7)

$(2, - 3)$ and $(- 4, - 7)$

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.

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

Step 3

Simplify.

Subtract $2$ from $- 4$ .

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

Raise $- 6$ to the power of $2$ .

$\sqrt{36 + {((- 7) - (- 3))}^{2}}$

Multiply $- 1$ by $- 3$ .

$\sqrt{36 + {(- 7 + 3)}^{2}}$

Add $- 7$ and $3$ .

$\sqrt{36 + {(- 4)}^{2}}$

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

$\sqrt{36 + 16}$

Add $36$ and $16$ .

$\sqrt{52}$

Rewrite $52$ as $2^{2} \cdot 13$ .

Factor $4$ out of $52$ .

$\sqrt{4 (13)}$

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

$\sqrt{2^{2} \cdot 13}$

Pull terms out from under the radical.

$2 \sqrt{13}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$2 \sqrt{13}$

Decimal Form:

$7.21110255 \dots$

Step 5