Chapter: Co-ordinate Geometry· Mathematics Part 2 (Geometry)
Answer: k = 6
The line bisects the segment, so it passes through the midpoint of the segment.
Midpoint of the segment joining (8, –1) and (0, k) \(= \left(\dfrac{8 + 0}{2}, \dfrac{-1 + k}{2}\right) = \left(4, \dfrac{k - 1}{2}\right)\)
This point lies on \(x - 6y + 11 = 0\):
\(4 - 6\left(\dfrac{k - 1}{2}\right) + 11 = 0\)
\(\therefore 15 - 3(k - 1) = 0\) \(\therefore 15 - 3k + 3 = 0\) \(\therefore 3k = 18\) \(\therefore k = 6\)