Find the Distance Between Two Points (8,7) and (1,-2)

$(8, 7)$ and $(1, - 2)$

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.

$\sqrt{{(1 - 8)}^{2} + {((- 2) - 7)}^{2}}$

Step 3

Simplify.

Subtract $8$ from $1$ .

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

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

$\sqrt{49 + {((- 2) - 7)}^{2}}$

Subtract $7$ from $- 2$ .

$\sqrt{49 + {(- 9)}^{2}}$

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

$\sqrt{49 + 81}$

Add $49$ and $81$ .

$\sqrt{130}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\sqrt{130}$

Decimal Form:

$11.40175425 \dots$

Step 5