Question

find the value of x if the distance between the points (x 1) and (2 3) be 4​

Answer 1

Answer :

x = 2 ± 2√3

Note :

• The distance between two points (x1,y1) and (x2,y2) is given by ;

d = √[(x2 - x1)² + (y2 - y1)²]

Solution :

Here ,

The given points are (x , 1) and (2 , 3) .

Also ,

It is given that , the distance between the given points is 4 units .

Now ,

Using the distance formula , the distance between the given points will be given as ;

=> d = √[(x2 - x1)² + (y2 - y1)²]

=> 4 = √[(2 - x)² + (3 - 1)²]

=> 4² = (2 - x)² + (3 - 1)²

=> 4² = (2 - x)² + 2²

=> 16 = (2 - x)² + 4

=> (2 - x)² = 16 - 4

=> (2 - x)² = 12

=> (x - 2)² = 12

=> x - 2 = √12

=> x - 2 = ±2√3

=> x = 2 ± 2√3

Hence , x = 2 ± 2√3 .