Find the Distance Between Two Points (2,4) , (-3,7)

$(2, 4)$ , $(- 3, 7)$

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.

$\sqrt{{((- 3) - 2)}^{2} + {(7 - 4)}^{2}}$

Step 3

Simplify.

Subtract $2$ from $- 3$ .

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

Raise $- 5$ to the power of $2$ .

$\sqrt{25 + {(7 - 4)}^{2}}$

Subtract $4$ from $7$ .

$\sqrt{25 + 3^{2}}$

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

$\sqrt{25 + 9}$

Add $25$ and $9$ .

$\sqrt{34}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\sqrt{34}$

Decimal Form:

$5.83095189 \dots$

Step 5