Find the Distance Between Two Points (-2,2.5) , (3,-2)

$(- 2, 2.5)$ , $(3, - 2)$

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.

$\sqrt{{(3 - (- 2))}^{2} + {((- 2) - 2.5)}^{2}}$

Step 3

Simplify.

Multiply $- 1$ by $- 2$ .

$\sqrt{{(3 + 2)}^{2} + {((- 2) - 2.5)}^{2}}$

Add $3$ and $2$ .

$\sqrt{5^{2} + {((- 2) - 2.5)}^{2}}$

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

$\sqrt{25 + {((- 2) - 2.5)}^{2}}$

Subtract $2.5$ from $- 2$ .

$\sqrt{25 + {(- 4.5)}^{2}}$

Raise $- 4.5$ to the power of $2$ .

$\sqrt{25 + 20.25}$

Add $25$ and $20.25$ .

$\sqrt{45.25}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\sqrt{45.25}$

Decimal Form:

$6.72681202 \dots$

Step 5