Find the Distance Between Two Points (0,4) , (7,2)

$(0, 4)$ , $(7, 2)$

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.

$\sqrt{{(7 - 0)}^{2} + {(2 - 4)}^{2}}$

Step 3

Simplify.

Subtract $0$ from $7$ .

$\sqrt{7^{2} + {(2 - 4)}^{2}}$

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

$\sqrt{49 + {(2 - 4)}^{2}}$

Subtract $4$ from $2$ .

$\sqrt{49 + {(- 2)}^{2}}$

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

$\sqrt{49 + 4}$

Add $49$ and $4$ .

$\sqrt{53}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\sqrt{53}$

Decimal Form:

$7.28010988 \dots$

Step 5