Find the Distance Between Two Points (8,-7) , (10,4)

$(8, - 7)$ , $(10, 4)$

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.

$\sqrt{{(10 - 8)}^{2} + {(4 - (- 7))}^{2}}$

Step 3

Simplify.

Subtract $8$ from $10$ .

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

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

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

Multiply $- 1$ by $- 7$ .

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

Add $4$ and $7$ .

$\sqrt{4 + 11^{2}}$

Raise $11$ to the power of $2$ .

$\sqrt{4 + 121}$

Add $4$ and $121$ .

$\sqrt{125}$

Rewrite $125$ as $5^{2} \cdot 5$ .

Factor $25$ out of $125$ .

$\sqrt{25 (5)}$

Rewrite $25$ as $5^{2}$ .

$\sqrt{5^{2} \cdot 5}$

Pull terms out from under the radical.

$5 \sqrt{5}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$5 \sqrt{5}$

Decimal Form:

$11.18033988 \dots$

Step 5