Find the Distance Between Two Points (-4,1) and (3,-4)

$(- 4, 1)$ and $(3, - 4)$

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.

$\sqrt{{(3 - (- 4))}^{2} + {((- 4) - 1)}^{2}}$

Step 3

Simplify.

Multiply $- 1$ by $- 4$ .

$\sqrt{{(3 + 4)}^{2} + {((- 4) - 1)}^{2}}$

Add $3$ and $4$ .

$\sqrt{7^{2} + {((- 4) - 1)}^{2}}$

Raise $7$ to the power of $2$ .

$\sqrt{49 + {((- 4) - 1)}^{2}}$

Subtract $1$ from $- 4$ .

$\sqrt{49 + {(- 5)}^{2}}$

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

$\sqrt{49 + 25}$

Add $49$ and $25$ .

$\sqrt{74}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\sqrt{74}$

Decimal Form:

$8.60232526 \dots$

Step 5