Find the Distance Between Two Points (-2,3) , (10,2)

$(- 2, 3)$ , $(10, 2)$

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.

$\sqrt{{(10 - (- 2))}^{2} + {(2 - 3)}^{2}}$

Step 3

Simplify.

Multiply $- 1$ by $- 2$ .

$\sqrt{{(10 + 2)}^{2} + {(2 - 3)}^{2}}$

Add $10$ and $2$ .

$\sqrt{12^{2} + {(2 - 3)}^{2}}$

Raise $12$ to the power of $2$ .

$\sqrt{144 + {(2 - 3)}^{2}}$

Subtract $3$ from $2$ .

$\sqrt{144 + {(- 1)}^{2}}$

Raise $- 1$ to the power of $2$ .

$\sqrt{144 + 1}$

Add $144$ and $1$ .

$\sqrt{145}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\sqrt{145}$

Decimal Form:

$12.04159457 \dots$

Step 5