Question

1. If (a,b) is the midpoint 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.

Answer 1

Given, (a,b) is the midpoint of the a(10,-6) and b(k,4). a-2b=18. we know that, Midpoint = (x1+x2/2), (y1+y2/2) (a,b)=(10+k/2),(-6+4/2) (a,b)=(10+k/2),(-2/2) (a,b)=(10+k/2),(-1) by comparing on both sides a=10+k/2 , b=-1 we know that, a-2b=18 => 10+k/2 -2(-1)=18 => 10+k/2+2=18 =>10+k/2=16 =>10+k=32 =>k=22