Find the Distance Between Two Points (5.3,8.2) , (-0.7,5.2)

$(5.3, 8.2)$ , $(- 0.7, 5.2)$

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.

$\sqrt{{((- 0.7) - 5.3)}^{2} + {(5.2 - 8.2)}^{2}}$

Step 3

Simplify.

Subtract $5.3$ from $- 0.7$ .

$\sqrt{{(- 6)}^{2} + {(5.2 - 8.2)}^{2}}$

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

$\sqrt{36 + {(5.2 - 8.2)}^{2}}$

Subtract $8.2$ from $5.2$ .

$\sqrt{36 + {(- 3)}^{2}}$

Raise $- 3$ to the power of $2$ .

$\sqrt{36 + 9}$

Add $36$ and $9$ .

$\sqrt{45}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\sqrt{45}$

Decimal Form:

$6.70820393 \dots$

Step 5