Question

if (a,b) is the mid-point of the line segment join the point a(10,-6) b (k ,4)and a-2b=18,find the value of k and the distance ab

Answer 1

The midpoint will be
$( \frac{10 + k}{2}and \: - 1)$
given a-2b =18
Therefore
$\frac{10 + k}{2} - 2 \times - 1 = 18 \\ 10 + k + 4 = 36 \\ k = 22$
and distance ab is
$\sqrt{ {(22 - 10)}^{2} + {(4 - - 6)}^{2} } \\ = \sqrt{ {12}^{2} + {10}^{2} } \\ = \sqrt{244}$
Hope this helps.