I am trying to teach myself A-level maths but have become a little stuck on the following quesion:
"The line $4x-5y+20 = 0$ cuts the x-axis at A and y-axis at B. Find the equation of the median through $O$ of triangle$OAB$."
I approached this by finding point A (-5,0) and B(0,4) and making a triangle using the origin (I assumed $O = $origin). I think the median of O is the same as the line which is perpendicular to $4x - 5y + 20 = 0$ and passes through the midpoint of $AB$. Doing this I got $10x + 8y - 41 = 0$ which I checked against an online calculator as correct.
However the answer in my book is $4x + 5y = 0$, so I feel I have misunderstood something pretty fundamental in the $Q$, but after looking around for a while I am no closer to understanding what.
Thanks for your help, Joe
"the median of O is the same as the line which is perpendicular to $4x - 5y + 20 = 0$" is incorrect and need not be considered.
The equation of the median will be thestraight line joining the midpoint of $AB$ and $O(0,0)$