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Chapter 8: Q27. (page 415)

Find the distance between the pair of points with the given coordinates $(9, - 2) and (12, - 14)$ .

Short Answer

Expert verified

The distance between the given pair of points is $3 \sqrt{17} units$ .

Step by step solution

01

Step 1. Write down the given information.

The given pair of points have coordinates $(9, - 2) and (12, - 14)$ .

02

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:

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

03

Step 3. Calculation.

The distance $(d)$ between the pair of points with given coordinates $(9, - 2) and (12, - 14)$ is evaluated using the formula (1) stated above.

\begin{matrix} |d| = \sqrt{{(x_{2} 鈭� x_{1})}^{2} + {(y_{2} 鈭� y_{1})}^{2}} \\ = \sqrt{{(12 鈭� 9)}^{2} + {(鈭� 14 + 2)}^{2}} \\ = \sqrt{{(3)}^{2} + {(鈭� 12)}^{2}} \\ = 3 \sqrt{17} units \end{matrix}

04

Step 4. Conclusion.

The distance between the given pair of points is $3 \sqrt{17} units$ .

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