Find the Distance Between Two Points (3,24) and (7,56)

$(3, 24)$ and $(7, 56)$

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.

$\sqrt{{(7 - 3)}^{2} + {(56 - 24)}^{2}}$

Step 3

Simplify.

Subtract $3$ from $7$ .

$\sqrt{4^{2} + {(56 - 24)}^{2}}$

Raise $4$ to the power of $2$ .

$\sqrt{16 + {(56 - 24)}^{2}}$

Subtract $24$ from $56$ .

$\sqrt{16 + 32^{2}}$

Raise $32$ to the power of $2$ .

$\sqrt{16 + 1024}$

Add $16$ and $1024$ .

$\sqrt{1040}$

Rewrite $1040$ as $4^{2} \cdot 65$ .

Factor $16$ out of $1040$ .

$\sqrt{16 (65)}$

Rewrite $16$ as $4^{2}$ .

$\sqrt{4^{2} \cdot 65}$

Pull terms out from under the radical.

$4 \sqrt{65}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$4 \sqrt{65}$

Decimal Form:

$32.24903099 \dots$

Step 5