Chapter 7: Q9. (page 356)

Which of the following point is closest to $(2, - 4)$ .
localid="1648636689763" $\begin{array}{l} (A) (3, 1) (B) (- 2, 0) \\ (C) (1, 5) (D) (4, - 2) \end{array}$

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 localid="1648636771543" $A (3, 1), B (- 2, 0), C (1, 5) and D (4, - 2)$ .

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

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

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

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

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.

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Which of the following point is closest to $(2, - 4)$ .
localid="1648636689763" $\begin{array}{l} (A) (3, 1) (B) (- 2, 0) \\ (C) (1, 5) (D) (4, - 2) \end{array}$

Short Answer

Step by step solution

Step 1. Write down the given information.

Step 2. Calculation.

Step 3. Conclusion.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Logic and Functions

Pure Maths

Probability and Statistics

Statistics

Theoretical and Mathematical Physics

Discrete Mathematics

Study anywhere. Anytime. Across all devices.

Which of the following point is closest to 2,-4.localid="1648636689763" A3,1B−2,0C1,5D4,−2

Short Answer

Step by step solution

Step 1. Write down the given information.

Step 2. Calculation.

Step 3. Conclusion.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Logic and Functions

Pure Maths

Probability and Statistics

Statistics

Theoretical and Mathematical Physics

Discrete Mathematics

Study anywhere. Anytime. Across all devices.

Which of the following point is closest to $(2, - 4)$ .
localid="1648636689763" $\begin{array}{l} (A) (3, 1) (B) (- 2, 0) \\ (C) (1, 5) (D) (4, - 2) \end{array}$