Find the Distance Between Two Points (-4,1) and (2,9)

$(- 4, 1)$ and $(2, 9)$

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.

$\sqrt{{(2 - (- 4))}^{2} + {(9 - 1)}^{2}}$

Step 3

Simplify.

Multiply $- 1$ by $- 4$ .

$\sqrt{{(2 + 4)}^{2} + {(9 - 1)}^{2}}$

Add $2$ and $4$ .

$\sqrt{6^{2} + {(9 - 1)}^{2}}$

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

$\sqrt{36 + {(9 - 1)}^{2}}$

Subtract $1$ from $9$ .

$\sqrt{36 + 8^{2}}$

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

$\sqrt{36 + 64}$

Add $36$ and $64$ .

$\sqrt{100}$

Rewrite $100$ as $10^{2}$ .

$\sqrt{10^{2}}$

Pull terms out from under the radical, assuming positive real numbers.

$10$

Step 4