Linear Algebra Examples

$(- 2, 6)$ , $(- 6, 3)$

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.

$\sqrt{{((- 6) - (- 2))}^{2} + {(3 - 6)}^{2}}$

Step 3

Simplify.

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Step 3.1

Multiply $- 1$ by $- 2$ .

$\sqrt{{(- 6 + 2)}^{2} + {(3 - 6)}^{2}}$

Step 3.2

Add $- 6$ and $2$ .

$\sqrt{{(- 4)}^{2} + {(3 - 6)}^{2}}$

Step 3.3

Raise $- 4$ to the power of $2$ .

$\sqrt{16 + {(3 - 6)}^{2}}$

Step 3.4

Subtract $6$ from $3$ .

$\sqrt{16 + {(- 3)}^{2}}$

Step 3.5

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

$\sqrt{16 + 9}$

Step 3.6

Add $16$ and $9$ .

$\sqrt{25}$

Step 3.7

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

$\sqrt{5^{2}}$

Step 3.8

Pull terms out from under the radical, assuming positive real numbers.

$5$

Step 4