Finite Math Examples

$(3, - 18)$ , $(10, y)$

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.

$\sqrt{{(10 - 3)}^{2} + {(y - (- 18))}^{2}}$

Step 3

Simplify.

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Step 3.1

Simplify the expression.

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Step 3.1.1

Subtract $3$ from $10$ .

$\sqrt{7^{2} + {(y - (- 18))}^{2}}$

Step 3.1.2

Raise $7$ to the power of $2$ .

$\sqrt{49 + {(y - (- 18))}^{2}}$

Step 3.1.3

Multiply $- 1$ by $- 18$ .

$\sqrt{49 + {(y + 18)}^{2}}$

Step 3.1.4

Rewrite ${(y + 18)}^{2}$ as $(y + 18) (y + 18)$ .

$\sqrt{49 + (y + 18) (y + 18)}$

Step 3.2

Expand $(y + 18) (y + 18)$ using the FOIL Method.

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Step 3.2.1

Apply the distributive property.

$\sqrt{49 + y (y + 18) + 18 (y + 18)}$

Step 3.2.2

Apply the distributive property.

$\sqrt{49 + y \cdot y + y \cdot 18 + 18 (y + 18)}$

Step 3.2.3

Apply the distributive property.

$\sqrt{49 + y \cdot y + y \cdot 18 + 18 y + 18 \cdot 18}$

Step 3.3

Simplify and combine like terms.

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Step 3.3.1

Simplify each term.

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Step 3.3.1.1

Multiply $y$ by $y$ .

$\sqrt{49 + y^{2} + y \cdot 18 + 18 y + 18 \cdot 18}$

Step 3.3.1.2

Move $18$ to the left of $y$ .

$\sqrt{49 + y^{2} + 18 \cdot y + 18 y + 18 \cdot 18}$

Step 3.3.1.3

Multiply $18$ by $18$ .

$\sqrt{49 + y^{2} + 18 y + 18 y + 324}$

Step 3.3.2

Add $18 y$ and $18 y$ .

$\sqrt{49 + y^{2} + 36 y + 324}$

Step 3.4

Add $49$ and $324$ .

$\sqrt{y^{2} + 36 y + 373}$