Chapter 8: Q33. (page 415)

Find the distance between the pair of points with the given coordinates $(\frac{2 \sqrt{3}}{3}, \frac{\sqrt{5}}{4}) and (- \frac{2 \sqrt{3}}{3}, \frac{\sqrt{5}}{2})$ .

Short Answer

Expert verified

The distance between the given pair of points is $\frac{\sqrt{813}}{12} units$ .

Step by step solution

Step 1. Write down the given information.

The given pair of points have coordinates $(\frac{2 \sqrt{3}}{3}, \frac{\sqrt{5}}{4}) and (- \frac{2 \sqrt{3}}{3}, \frac{\sqrt{5}}{2})$ .

Step 2. Concept used.

If a line segment has end-points at $(x_{1}, y_{1}) and (x_{2}, y_{2})$ then the distance $(d)$ between these points is given as:

$|d| = \sqrt{{(x_{2} - x_{1})}^{2} + {(y_{2} - y_{1})}^{2}} . . . . (1)$

Step 3. Calculation.

The distance $(d)$ between the pair of points with given coordinates $(\frac{2 \sqrt{3}}{3}, \frac{\sqrt{5}}{4}) and (- \frac{2 \sqrt{3}}{3}, \frac{\sqrt{5}}{2})$ is evaluated using the formula (1) stated above.

\begin{matrix} |d| = \sqrt{{(x_{2} - x_{1})}^{2} + {(y_{2} - y_{1})}^{2}} \\ = \sqrt{{(- \frac{2 \sqrt{3}}{3} - \frac{2 \sqrt{3}}{3})}^{2} + {(\frac{\sqrt{5}}{2} - \frac{\sqrt{5}}{4})}^{2}} \\ = \sqrt{{(- \frac{4 \sqrt{3}}{3})}^{2} + {(\frac{\sqrt{5}}{4})}^{2}} \\ = \frac{\sqrt{813}}{12} units \end{matrix}

Step 4. Conclusion.

The distance between the given pair of points is $\frac{\sqrt{813}}{12} units$ $\frac{\sqrt{813}}{12} units$ .

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Find the distance between the pair of points with the given coordinates $(\frac{2 \sqrt{3}}{3}, \frac{\sqrt{5}}{4}) and (- \frac{2 \sqrt{3}}{3}, \frac{\sqrt{5}}{2})$ .

Short Answer

Step by step solution

Step 1. Write down the given information.

Step 2. Concept used.

Step 3. Calculation.

Step 4. Conclusion.

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Find the distance between the pair of points with the given coordinates 233,54and-233,52.

Short Answer

Step by step solution

Step 1. Write down the given information.

Step 2. Concept used.

Step 3. Calculation.

Step 4. Conclusion.

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Most popular questions from this chapter

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Study anywhere. Anytime. Across all devices.

Find the distance between the pair of points with the given coordinates $(\frac{2 \sqrt{3}}{3}, \frac{\sqrt{5}}{4}) and (- \frac{2 \sqrt{3}}{3}, \frac{\sqrt{5}}{2})$ .