Chapter 10: Q19. (page 661)

Find the distance between the points with the given coordinate.
$(- 4, - 6), (- 7, 1)$

Short Answer

Expert verified

The distance between the coordinates $(- 4, - 6)$ and $(- 7, 1)$ is 5 units.

Step by step solution

Step 1. State the concept of ‘Distance between two points in 2 dimensional plane’.

Let the two points in 2 dimensional plane be $(x_{1}, y_{1})$ and $(x_{2}, y_{2})$ .

The distance between the points is given as:

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

Where $d$ is the distance.

Step 2. Calculate the distance.

The two points which is given are $(- 4, - 6)$ and $(- 7, 1)$ .

Substitute $(- 4, - 6)$ as $(x_{1}, y_{1})$ and $(- 7, 1)$ as $(x_{2}, y_{2})$ in $(1)$ to calculate the distance.

$\begin{array}{l} d = \sqrt{{(x_{2} - x_{1})}^{2} + {(y_{2} - y_{1})}^{2}} \\ = \sqrt{{(- 7 - (- 4))}^{2} + {(1 - (- 6))}^{2}} \\ = \sqrt{{(- 7 + 4)}^{2} + {(1 + 6)}^{2}} \\ = \sqrt{{(- 3)}^{2} + {(7)}^{2}} \\ = \sqrt{9 + 49} \\ = \sqrt{58} \end{array}$

Step 3. State the conclusion.

Therefore, distance between the points $(- 4, - 6)$ and $(- 7, 1)$ is $\sqrt{58}$ units.

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Find the distance between the points with the given coordinate.
$(- 4, - 6), (- 7, 1)$

Short Answer

Step by step solution

Step 1. State the concept of ‘Distance between two points in 2 dimensional plane’.

Step 2. Calculate the distance.

Step 3. State the conclusion.

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Find the distance between the points with the given coordinate.(−4,−6), (−7,1)

Short Answer

Step by step solution

Step 1. State the concept of ‘Distance between two points in 2 dimensional plane’.

Step 2. Calculate the distance.

Step 3. State the conclusion.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Pure Maths

Discrete Mathematics

Geometry

Theoretical and Mathematical Physics

Applied Mathematics

Mechanics Maths

Study anywhere. Anytime. Across all devices.

Find the distance between the points with the given coordinate.
$(- 4, - 6), (- 7, 1)$