Question

Find the value of k when the distance between A(3, k) and B(4,1) is $\sqrt{10}$ unit.

Answer 1

Solution :

*************************************

We know,

the distance between two points

A( x1 , y1 ) and B( x2 , y2 ) is

√( x2 - x1 )² + ( y2 - y1 )²

**************************************

Let A( x1, y1 ) = ( 3, k ),

B( x2 , y2 ) = ( 4 , 1 )

Distance between A and B = √10

=> ( x2 - x1 )² + ( y2 - y1 )² = ( √10 )²

=> ( 4 - 3 )² + ( 1 - k )² = 10

=> 1 + ( 1 - k )² = 10

=> ( k - 1 )² = 9

=> k - 1 = ± 3

=> k = 1 ± 3

=> k = 1+3 or k = 1 - 3

Therefore ,

k = 4 or k = -2

•••••