Find the Distance Between Two Points (2,-3) , (2,4)

$(2, - 3)$ , $(2, 4)$

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.

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

Step 3

Simplify.

Subtract $2$ from $2$ .

$\sqrt{0^{2} + {(4 - (- 3))}^{2}}$

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

$\sqrt{0 + {(4 - (- 3))}^{2}}$

Multiply $- 1$ by $- 3$ .

$\sqrt{0 + {(4 + 3)}^{2}}$

Add $4$ and $3$ .

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

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