Find the Distance Between Two Points (-1,2) and (2,-4)

$(- 1, 2)$ and $(2, - 4)$

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.

$\sqrt{{(2 - (- 1))}^{2} + {((- 4) - 2)}^{2}}$

Step 3

Simplify.

Multiply $- 1$ by $- 1$ .

$\sqrt{{(2 + 1)}^{2} + {((- 4) - 2)}^{2}}$

Add $2$ and $1$ .

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

Raise $3$ to the power of $2$ .

$\sqrt{9 + {((- 4) - 2)}^{2}}$

Subtract $2$ from $- 4$ .

$\sqrt{9 + {(- 6)}^{2}}$

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

$\sqrt{9 + 36}$

Add $9$ and $36$ .

$\sqrt{45}$

Rewrite $45$ as $3^{2} \cdot 5$ .

Factor $9$ out of $45$ .

$\sqrt{9 (5)}$

Rewrite $9$ as $3^{2}$ .

$\sqrt{3^{2} \cdot 5}$

Pull terms out from under the radical.

$3 \sqrt{5}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$3 \sqrt{5}$

Decimal Form:

$6.70820393 \dots$

Step 5