Find the equation of the line through M (-1,2) with gradient m if M is the midpoint of the intercepts of the x axis and y axis
equation of line = y - y1 = m ( x - x1)
what next I am confused with the midpoint of axis.
Thanks
Hello Joel,
your line passes through the point , so you know that (using the standard equation )
Now, let be the intercept of the y-axis, and be the intercept of the x-axis. Then we have . Thus we have and . Since these are intercepts, we can get some more information :
(using )
Now recover the equation we found first :
Solving the two equations simultaneously :
And the equation of the line follows :
Plotting this line indeed shows that it passes through , and that this point is exactly midpoint between the x-intercept and y-intercept of the line
Don't hesitate to reply if anything seems confusing.
Hi bacterius,
After reading your first paragraph I accepted this as your proof of the x and y intercepts of the required line ie that the x intercept is -2 and y intercept is 4. So immediately y=2x+4. Was it necessary to go further. I did it by taking a straight edge and rotating it about M so that M was the midpoint between the x and y axis
bjh