Find the Distance Between Two Points (-4,1) , (-4,8)

$(- 4, 1)$ , $(- 4, 8)$

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.

$\sqrt{{((- 4) - (- 4))}^{2} + {(8 - 1)}^{2}}$

Step 3

Simplify.

Multiply $- 1$ by $- 4$ .

$\sqrt{{(- 4 + 4)}^{2} + {(8 - 1)}^{2}}$

Add $- 4$ and $4$ .

$\sqrt{0^{2} + {(8 - 1)}^{2}}$

Raising $0$ to any positive power yields $0$ .

$\sqrt{0 + {(8 - 1)}^{2}}$

Subtract $1$ from $8$ .

$\sqrt{0 + 7^{2}}$

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

$\sqrt{0 + 49}$

Add $0$ and $49$ .

$\sqrt{49}$

Rewrite $49$ as $7^{2}$ .

$\sqrt{7^{2}}$

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

$7$

Step 4