# Find the distance between the following pairs of points:

$

\left( i \right){\text{ }}\left( {2,3} \right),\left( {4,1} \right) \\

\left( {ii} \right){\text{ }}\left( { - 5,7} \right),\left( { - 1,3} \right) \\

\left( {iii} \right){\text{ }}\left( {a,b} \right),\left( { - a, - b} \right) \\

$

Answer

Verified

364.5k+ views

Hint – Whenever we are given two points, we can easily find the distance between them using the concept of distance formula. Use this same concept to find distance for all three options.

Whenever we are given two pair of point such that the points are $\left( {{x_1},{y_1}} \right){\text{ and }}\left( {{x_2},{y_2}} \right)$ then the distance between these points can be given as $\sqrt {{{\left( {{x_2} - {x_1}} \right)}^2} + {{\left( {{y_2} - {y_1}} \right)}^2}} $……………. (1)

Now the first pair of point is $\left( i \right){\text{ }}\left( {2,3} \right),\left( {4,1} \right)$

Using equation (1) we get

Distance = $\sqrt {{{\left( {4 - 2} \right)}^2} + {{\left( {1 - 3} \right)}^2}} $

Distance= $\sqrt {{2^2} + {{\left( { - 2} \right)}^2}} $

$ \Rightarrow \sqrt {4 + 4} = 2\sqrt 2 $ m

Now the second pair of point is $\left( {ii} \right){\text{ }}\left( { - 5,7} \right),\left( { - 1,3} \right)$

Using equation (1) we get

Distance = $\sqrt {{{\left( { - 1 - \left( { - 5} \right)} \right)}^2} + {{\left( {3 - 7} \right)}^2}} $

Distance= $\sqrt {{4^2} + {{\left( { - 4} \right)}^2}} $

$ \Rightarrow \sqrt {16 + 16} = 4\sqrt 2 $ m

Now the second pair of point is $\left( {iii} \right){\text{ }}\left( {a,b} \right),\left( { - a, - b} \right)$

Using equation (1) we get

Distance = $\sqrt {{{\left( { - a - \left( a \right)} \right)}^2} + {{\left( { - b - b} \right)}^2}} $

Distance= $\sqrt {{{\left( { - 2a} \right)}^2} + {{\left( { - 2b} \right)}^2}} $

$ \Rightarrow \sqrt {4{a^2} + 4{b^2}} = 2\sqrt {{a^2} + {b^2}} $ m

Note – Whenever we face such type of problems, the key concept is compare the given points whose distance is to be calculated with any general point $\left( {{x_1},{y_1}} \right){\text{ and }}\left( {{x_2},{y_2}} \right)$ and then applying the distance formula to obtain the right distance between them.

Whenever we are given two pair of point such that the points are $\left( {{x_1},{y_1}} \right){\text{ and }}\left( {{x_2},{y_2}} \right)$ then the distance between these points can be given as $\sqrt {{{\left( {{x_2} - {x_1}} \right)}^2} + {{\left( {{y_2} - {y_1}} \right)}^2}} $……………. (1)

Now the first pair of point is $\left( i \right){\text{ }}\left( {2,3} \right),\left( {4,1} \right)$

Using equation (1) we get

Distance = $\sqrt {{{\left( {4 - 2} \right)}^2} + {{\left( {1 - 3} \right)}^2}} $

Distance= $\sqrt {{2^2} + {{\left( { - 2} \right)}^2}} $

$ \Rightarrow \sqrt {4 + 4} = 2\sqrt 2 $ m

Now the second pair of point is $\left( {ii} \right){\text{ }}\left( { - 5,7} \right),\left( { - 1,3} \right)$

Using equation (1) we get

Distance = $\sqrt {{{\left( { - 1 - \left( { - 5} \right)} \right)}^2} + {{\left( {3 - 7} \right)}^2}} $

Distance= $\sqrt {{4^2} + {{\left( { - 4} \right)}^2}} $

$ \Rightarrow \sqrt {16 + 16} = 4\sqrt 2 $ m

Now the second pair of point is $\left( {iii} \right){\text{ }}\left( {a,b} \right),\left( { - a, - b} \right)$

Using equation (1) we get

Distance = $\sqrt {{{\left( { - a - \left( a \right)} \right)}^2} + {{\left( { - b - b} \right)}^2}} $

Distance= $\sqrt {{{\left( { - 2a} \right)}^2} + {{\left( { - 2b} \right)}^2}} $

$ \Rightarrow \sqrt {4{a^2} + 4{b^2}} = 2\sqrt {{a^2} + {b^2}} $ m

Note – Whenever we face such type of problems, the key concept is compare the given points whose distance is to be calculated with any general point $\left( {{x_1},{y_1}} \right){\text{ and }}\left( {{x_2},{y_2}} \right)$ and then applying the distance formula to obtain the right distance between them.

Last updated date: 26th Sep 2023

•

Total views: 364.5k

•

Views today: 3.64k

Recently Updated Pages

What do you mean by public facilities

Slogan on Noise Pollution

Paragraph on Friendship

Disadvantages of Advertising

Prepare a Pocket Guide on First Aid for your School

What is the Full Form of ILO, UNICEF and UNESCO

Trending doubts

How do you solve x2 11x + 28 0 using the quadratic class 10 maths CBSE

Summary of the poem Where the Mind is Without Fear class 8 english CBSE

The poet says Beauty is heard in Can you hear beauty class 6 english CBSE

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE

Difference Between Plant Cell and Animal Cell

Fill the blanks with the suitable prepositions 1 The class 9 english CBSE

What is the past tense of read class 10 english CBSE

The equation xxx + 2 is satisfied when x is equal to class 10 maths CBSE

Differentiate between homogeneous and heterogeneous class 12 chemistry CBSE