Question

If (a,b) is mid point of 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.

Answer 1

Since (a,b) is mid point so

(a,b) = { (10+k)/2 , (-6+4)/2}

here,
a = (10+k)/2
and
b= -2/2 = -1
put a=(10-k)/2 and b=-5 in a-2b=18


(10+k)/2-2 (-1) =18

10+k+2=36
k= 36-12 = 24

now
AB =
$\sqrt{(x2 - x1) {}^{2}(y2 - y1) {}^{2} }$
$= \sqrt{(24 - 10) {}^{2}(6 + 4) {}^{2} }$
$= \sqrt{14 {}^{2} \times 10 {}^{2} }$
= 14×10
= 140

hope it helps you