Find the Distance Between Two Points (7,4) and (4,-5)

$(7, 4)$ and $(4, - 5)$

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.

$\sqrt{{(4 - 7)}^{2} + {((- 5) - 4)}^{2}}$

Step 3

Simplify.

Subtract $7$ from $4$ .

$\sqrt{{(- 3)}^{2} + {((- 5) - 4)}^{2}}$

Raise $- 3$ to the power of $2$ .

$\sqrt{9 + {((- 5) - 4)}^{2}}$

Subtract $4$ from $- 5$ .

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

Raise $- 9$ to the power of $2$ .

$\sqrt{9 + 81}$

Add $9$ and $81$ .

$\sqrt{90}$

Rewrite $90$ as $3^{2} \cdot 10$ .

Factor $9$ out of $90$ .

$\sqrt{9 (10)}$

Rewrite $9$ as $3^{2}$ .

$\sqrt{3^{2} \cdot 10}$

Pull terms out from under the radical.

$3 \sqrt{10}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$3 \sqrt{10}$

Decimal Form:

$9.48683298 \dots$

Step 5