Algebra Examples

$(0, a)$ , $(a, 0)$

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.

$\sqrt{{(a - 0)}^{2} + {(0 - a)}^{2}}$

Step 3

Simplify.

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Step 3.1

Simplify the expression.

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Step 3.1.1

Subtract $0$ from $a$ .

$\sqrt{a^{2} + {(0 - a)}^{2}}$

Step 3.1.2

Subtract $a$ from $0$ .

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

Step 3.1.3

Apply the product rule to $- a$ .

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

Step 3.1.4

Raise $- 1$ to the power of $2$ .

$\sqrt{a^{2} + 1 a^{2}}$

Step 3.1.5

Multiply $a^{2}$ by $1$ .

$\sqrt{a^{2} + a^{2}}$

Step 3.2

Add $a^{2}$ and $a^{2}$ .

$\sqrt{2 a^{2}}$

Step 3.3

Reorder $2$ and $a^{2}$ .

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

Step 3.4

Pull terms out from under the radical.

$a \sqrt{2}$