Find the Distance Between Two Points (-2 1/2,-3) , (1,-3)

$(- 2 \frac{1}{2}, - 3)$ , $(1, - 3)$

Step 1

Convert $2 \frac{1}{2}$ to an improper fraction.

A mixed number is an addition of its whole and fractional parts.

$(- (2 + \frac{1}{2}), - 3) - (1, - 3)$

Add $2$ and $\frac{1}{2}$ .

To write $2$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$(- (2 \cdot \frac{2}{2} + \frac{1}{2}), - 3) - (1, - 3)$

Combine $2$ and $\frac{2}{2}$ .

$(- (\frac{2 \cdot 2}{2} + \frac{1}{2}), - 3) - (1, - 3)$

Combine the numerators over the common denominator.

$(- \frac{2 \cdot 2 + 1}{2}, - 3) - (1, - 3)$

Simplify the numerator.

Multiply $2$ by $2$ .

$(- \frac{4 + 1}{2}, - 3) - (1, - 3)$

Add $4$ and $1$ .

$(- \frac{5}{2}, - 3) - (1, - 3)$

Step 2

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 3

Substitute the actual values of the points into the distance formula.

$\sqrt{{(1 - (- \frac{5}{2}))}^{2} + {((- 3) - (- 3))}^{2}}$

Step 4

Simplify.

Multiply $- (- \frac{5}{2})$ .

Multiply $- 1$ by $- 1$ .

$\sqrt{{(1 + 1 (\frac{5}{2}))}^{2} + {((- 3) - (- 3))}^{2}}$

Multiply $\frac{5}{2}$ by $1$ .

$\sqrt{{(1 + \frac{5}{2})}^{2} + {((- 3) - (- 3))}^{2}}$

Write $1$ as a fraction with a common denominator.

$\sqrt{{(\frac{2}{2} + \frac{5}{2})}^{2} + {((- 3) - (- 3))}^{2}}$

Combine the numerators over the common denominator.

$\sqrt{{(\frac{2 + 5}{2})}^{2} + {((- 3) - (- 3))}^{2}}$

Add $2$ and $5$ .

$\sqrt{{(\frac{7}{2})}^{2} + {((- 3) - (- 3))}^{2}}$

Apply the product rule to $\frac{7}{2}$ .

$\sqrt{\frac{7^{2}}{2^{2}} + {((- 3) - (- 3))}^{2}}$

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

$\sqrt{\frac{49}{2^{2}} + {((- 3) - (- 3))}^{2}}$

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

$\sqrt{\frac{49}{4} + {((- 3) - (- 3))}^{2}}$

Multiply $- 1$ by $- 3$ .

$\sqrt{\frac{49}{4} + {(- 3 + 3)}^{2}}$

Add $- 3$ and $3$ .

$\sqrt{\frac{49}{4} + 0^{2}}$

Raising $0$ to any positive power yields $0$ .

$\sqrt{\frac{49}{4} + 0}$

Add $\frac{49}{4}$ and $0$ .

$\sqrt{\frac{49}{4}}$

Rewrite $\sqrt{\frac{49}{4}}$ as $\frac{\sqrt{49}}{\sqrt{4}}$ .

$\frac{\sqrt{49}}{\sqrt{4}}$

Simplify the numerator.

Rewrite $49$ as $7^{2}$ .

$\frac{\sqrt{7^{2}}}{\sqrt{4}}$

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

$\frac{7}{\sqrt{4}}$

Simplify the denominator.

Rewrite $4$ as $2^{2}$ .

$\frac{7}{\sqrt{2^{2}}}$

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

$\frac{7}{2}$

Step 5

Find the Distance Between Two Points (-2 1/2,-3) , (1,-3)

Related Questions