Question

In a standard rectangular system of axes, what are the values of k so that the distance between point A(k, −2) and point B(3, −4) is equal to √7?

Answer 1

Distance Formula between 2 points A (p,q) and B (x,y) on a rectangular coordinate system or on coordinate axis is ,

• √ { ( a-x )² + ( b-y )² }

=> Now , the distance between (k,-2) and (3,-4) is √7 .

=> √ 7 = √ { ( k-3 )² + ( -4-(-2) )² }

Squaring both sides ,

=> 7 = (k-3)² + (-2)²

=> 7-4 = 3 = (k-3)²

=> Taking square root , both sides ,

=> √3 = k - 3

=> k = ( 3+√3 )

Answer is k = ( 3+√3 )