Find the Distance Between Two Points (-4,5) and (4,0)

$(- 4, 5)$ and $(4, 0)$

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.

$\sqrt{{(4 - (- 4))}^{2} + {(0 - 5)}^{2}}$

Step 3

Simplify.

Multiply $- 1$ by $- 4$ .

$\sqrt{{(4 + 4)}^{2} + {(0 - 5)}^{2}}$

Add $4$ and $4$ .

$\sqrt{8^{2} + {(0 - 5)}^{2}}$

Raise $8$ to the power of $2$ .

$\sqrt{64 + {(0 - 5)}^{2}}$

Subtract $5$ from $0$ .

$\sqrt{64 + {(- 5)}^{2}}$

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

$\sqrt{64 + 25}$

Add $64$ and $25$ .

$\sqrt{89}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\sqrt{89}$

Decimal Form:

$9.43398113 \dots$

Step 5