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

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

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.

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

Step 3

Simplify.

Multiply $- 1$ by $- 1$ .

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

Add $1$ and $1$ .

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

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

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

Subtract $4$ from $- 1$ .

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

Raise $- 5$ to the power of $2$ .

$\sqrt{4 + 25}$

Add $4$ and $25$ .

$\sqrt{29}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\sqrt{29}$

Decimal Form:

$5.38516480 \dots$

Step 5