Question

find the distance between the following pairs of points (2,3), (4,1)

For moderator
Brainly ⭐
Other best users

Answer 1

Question :-

find the distance between the following pairs of points (2,3), (4,1)

Given that :-

• Points = (2,3), (4,1)

To Find :-

• Distance between the following pairs of points ?

Solution :-

Here,

• ${ \rm{x_{1} = 2}}$
• ${ \rm{x_{2} = 4}}$
• ${ \rm{y_{1} = 3}}$
• ${ \rm{y_{2} = 1}}$

Distance between two points is calculated by using the formula given below :-

${ \boxed{ \pink{\rm Distance\ =\ \sqrt{(x_2\ -\ x_1)^2\ +\ (y_2\ -\ y_1)^2}}}}$

Substitute the value in the formula : we get,

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

${\rm Distance\ =\ \sqrt{(2)^2\ +\ (2)^2}}$

${\rm Distance\ =\ \sqrt{4 + 4}}$

${\rm Distance\ =\ \sqrt{8}}$

${\rm Distance\ =\ \sqrt{4 \times (2)}}$

${\rm Distance\ =\ \sqrt{4} \times \sqrt{2} }$

${\rm Distance\ =\ 2 \times \sqrt{2} }$

${\rm Distance\ =\ 2\sqrt{2} \: units}$

Therefore, the distance between (2,3) and (4,1) is 2√2 units.

Answer 2

A(2,3)

B(4,1)

Let's assume

$\sf \red{x_1}$=2

$\sf \red{y_1}$=3

$\sf \red{x_2}$=4

$\sf \red{y_2}$=1

∴${ \blue{\rm Distance\ =\ \sqrt{(x_2\ -\ x_1)^2\ +\ (y_2\ -\ y_1)^2}}}$

∴${ \red{\rm Distance\ =\ \sqrt{(4\ -\ 2)^2\ +\ (1\ -\ 3)^2}}}$

∴${ \green{\rm Distance\ =\ \sqrt{(2)^2\ +\ (-2)^2}}}$

∴${ \pink{\rm Distance\ =\ \sqrt{4+\ 4}}}$

∴${ \orange{\rm Distance\ =\ \sqrt{8}}}$

∴Distance=2×2×2

∴Distance=2√2 units