Find the Distance Between Two Points (7,1) , (-4,-5)

$(7, 1)$ , $(- 4, - 5)$

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.

$\sqrt{{((- 4) - 7)}^{2} + {((- 5) - 1)}^{2}}$

Step 3

Simplify.

Subtract $7$ from $- 4$ .

$\sqrt{{(- 11)}^{2} + {((- 5) - 1)}^{2}}$

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

$\sqrt{121 + {((- 5) - 1)}^{2}}$

Subtract $1$ from $- 5$ .

$\sqrt{121 + {(- 6)}^{2}}$

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

$\sqrt{121 + 36}$

Add $121$ and $36$ .

$\sqrt{157}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\sqrt{157}$

Decimal Form:

$12.52996408 \dots$

Step 5