Question

Find the distance between the points (√5 -2, √3+2) and (√5 +1, √3 -1)

Answer 1

Use distance formula , i.e

The distance between two points (x1,y1) and (x2,y2) can be calculated by using distance formula


√{(x2-x1)^2 +(y2-y1)^2}

Now according to your question let x1= √5-2

y1= √3+2

x2 = √5+1

y2= √3-1

Now substitute these values in the equation


√{(x2-x1)^2 +(y2-y1)^2}


√{(√5+1-(√5-2))^2 +(√3-1-(√3+2))^2}

You will get the answer as 3 √2

Answer 2

Given :

• Two points A ( √5 - 2 , √3 + 2 ) and B ( √5 + 1 , √3 - 1 )

To find :

• Distance between points A and B

Formulae required :

• Distance formula

AB = √ [ ( x₁ - x₂ )² + ( y₁ - y₂ )² ]

[ where A is a point with coordinates ( x₁ , y₁ ) and B is a point with coordinates ( x₂ , y₂ ) and AB is distance between the points ]

Solution :

Using distance formula

→ AB = √[ { (√5 - 2) - (√5 + 1) }² + { (√3 + 2) -  (√3 - 1)² }² ]

→ AB = √[ {√5 - 2 - √5 - 1}² + {√3 + 2 - √3 + 1 }² ]

→ AB = √[ {-3}² + {3}² ]

→ AB = √[ 9 + 9 ]

→ AB = √18  units

Therefore,

• Distance between given two points will be √18 units .