Find the Distance Between Two Points (2,-5) and (7,4)

$(2, - 5)$ and $(7, 4)$

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.

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

Step 3

Simplify.

Subtract $2$ from $7$ .

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

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

$\sqrt{25 + {(4 - (- 5))}^{2}}$

Multiply $- 1$ by $- 5$ .

$\sqrt{25 + {(4 + 5)}^{2}}$

Add $4$ and $5$ .

$\sqrt{25 + 9^{2}}$

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

$\sqrt{25 + 81}$

Add $25$ and $81$ .

$\sqrt{106}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\sqrt{106}$

Decimal Form:

$10.29563014 \dots$

Step 5