Question

Find the distance between the pair of points
(2,3) (4,1)

Answer 1

Answer:

Distance between the pair of given points is 2√2 units.

Step-by-step explanation:

We know that,

$\red{ \sf{distance \: = \sqrt{ {({x_2} - {x_1})}^{2} + \: {({y_2} - {y_1})}^{2} }}}$

Putting the values,

$\implies$ Distance = $\sf{\sqrt{ {({4} - {2})}^{2} + \: {({1} - {3})}^{2} }}$

$\implies$ Distance = $\sf{\sqrt{(2)^2\:+\:(-2)^2}}$

$\implies$ Distance = $\sf{\sqrt{4+4}}$

$\implies$ Distance = $\sf{\sqrt{8}}$

$\implies$ Distance = $\sf{2\:\sqrt{2}}$

$\therefore$ Distance between the pair of given points is 2√2 units.

Answer 2

Solution

AB = 2√2 units

Given

Let the given points be A(2,3) and B(4,1)

To finD

The value of AB

Distance Formula

$\displaystyle{\sf \sqrt{(x_2 - x_1)^{2} +(y_2 - y_1)^2 } }$

Substituting the values,we get :

$\sf \: \sqrt{(4 - 2) {}^{2} + (1 - 3) {}^{2} } \\ \\ \implies \: \sf \: \sqrt{ {2}^{2} + {( - 2)}^{2} } \\ \\ \implies \: \sf \: \sqrt{4 + 4} \implies \: \sqrt{8} \implies \: 2 \sqrt{2} \: \: units$