If (a, b) is the mid - point of the line segment joining the points A(10, - 6), B(k, 4) and a – 2b = 18, then find the value of k and the distance AB.


Given,

(a, b) is the mid - point of line segment AB


Since, mid - point of a line segment having points (x1, y1) and (x2, y2) =


So,



(a, b) =


Now, equating coordinates on both sides, we get


a = …. (i)


And


b = - 1 …(ii)


Given,


a – 2b = 18


Using equation (ii);


a – 2( - 1) = 18


a + 2 = 18


a = 16


Using equation (i);


16 =


32 = 10 + k


k = 22


Hence, the required value of k is 22


k = 22


A = (10, - 6),


B = (22, 4)


Now,


By using the distance formula;


Distance between two points (x1, y1) and (x2, y2);



So,


Distance between A (10, - 6) and B (22, 4)


AB =


=


Hence, the distance of AB is


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