Find the Distance Between Two Points (5,2) and (-1,9)

$(5, 2)$ and $(- 1, 9)$

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.

$\sqrt{{((- 1) - 5)}^{2} + {(9 - 2)}^{2}}$

Step 3

Simplify.

Subtract $5$ from $- 1$ .

$\sqrt{{(- 6)}^{2} + {(9 - 2)}^{2}}$

Raise $- 6$ to the power of $2$ .

$\sqrt{36 + {(9 - 2)}^{2}}$

Subtract $2$ from $9$ .

$\sqrt{36 + 7^{2}}$

Raise $7$ to the power of $2$ .

$\sqrt{36 + 49}$

Add $36$ and $49$ .

$\sqrt{85}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\sqrt{85}$

Decimal Form:

$9.21954445 \dots$

Step 5