Q9. Which of the following point is ... [FREE SOLUTION]

Chapter 8: Q9. (page 414)

Which of the following point is closest to $(2, - 4)$ .
role="math" localid="1648203269021" $\begin{array}{l} (A) (3, 1) (B) (鈭� 2, 0) \\ (C) (1, 5) (D) (4, 鈭� 2) \end{array}$

Short Answer

Expert verified

The distance of point $P (2, - 4)$ from the point $D (4, - 2)$ is least.Hence the point $P (2, - 4)$ is closest to $D (4, - 2)$ . So, option (D) is correct.

Step by step solution

Step 1. Write down the given information.

The given points are $A (3, 1), B (- 2, 0), C (1, 5) and D (4, - 2)$ whose distance from the fixed point say $P (2, - 4)$ has to determine.

Step 2. Calculation.

The distance $(d)$ from the point $P (2, - 4)$ is evaluated from the points $A (3, 1), B (- 2, 0), C (1, 5) and D (4, - 2)$ .

\begin{matrix} |d_{P A}| = \sqrt{{(x_{2} 鈭� x_{1})}^{2} + {(y_{2} 鈭� y_{1})}^{2}} \\ = \sqrt{{(3 鈭� 2)}^{2} + {(1 + 4)}^{2}} \\ = \sqrt{26} units \end{matrix}

\begin{matrix} |d_{P B}| = \sqrt{{(x_{2} 鈭� x_{1})}^{2} + {(y_{2} 鈭� y_{1})}^{2}} \\ = \sqrt{{(鈭� 2 鈭� 2)}^{2} + {(0 + 4)}^{2}} \\ = 4 \sqrt{2} units \end{matrix}

\begin{matrix} |d_{P C}| = \sqrt{{(x_{2} 鈭� x_{1})}^{2} + {(y_{2} 鈭� y_{1})}^{2}} \\ = \sqrt{{(1 鈭� 2)}^{2} + {(5 + 4)}^{2}} \\ = \sqrt{82} units \end{matrix}

\begin{matrix} |d_{P D}| = \sqrt{{(x_{2} 鈭� x_{1})}^{2} + {(y_{2} 鈭� y_{1})}^{2}} \\ = \sqrt{{(4 鈭� 2)}^{2} + {(鈭� 2 + 4)}^{2}} \\ = 2 \sqrt{2} units \end{matrix}

Step 3. Conclusion.

The distance of point $P (2, - 4)$ from the point $D (4, - 2)$ is least. Hence the point $P (2, - 4)$ is closest to $D (4, - 2)$ . So, option (D) is correct.

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Which of the following point is closest to $(2, - 4)$ .
role="math" localid="1648203269021" $\begin{array}{l} (A) (3, 1) (B) (鈭� 2, 0) \\ (C) (1, 5) (D) (4, 鈭� 2) \end{array}$

Short Answer

Step by step solution

Step 1. Write down the given information.

Step 2. Calculation.

Step 3. Conclusion.

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Which of the following point is closest to2,-4.role="math" localid="1648203269021" A3,1B鈭�2,0C1,5D4,鈭�2

Short Answer

Step by step solution

Step 1. Write down the given information.

Step 2. Calculation.

Step 3. Conclusion.

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Most popular questions from this chapter

Recommended explanations on Math Textbooks

Mechanics Maths

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Study anywhere. Anytime. Across all devices.

Which of the following point is closest to $(2, - 4)$ .
role="math" localid="1648203269021" $\begin{array}{l} (A) (3, 1) (B) (鈭� 2, 0) \\ (C) (1, 5) (D) (4, 鈭� 2) \end{array}$