The sides AB,BC,CA lie on the lines 2y=x-4,x+y=5 and y=mx respectively. If the the origin O is the midpoint of AC , find the value of M

Question

The sides AB,BC,CA lie on the lines 2y=x-4,x+y=5 and y=mx respectively. If the the origin O is the midpoint of AC , find the value of M How can i find the coordinates of O if I don't know the coordinate of AC?

Answer 1

Substitute $y=mx $ into $2y=x-4,\>x+y=5$ to get

$$ 2mx_1=x_1-4,\>\>\>\>\> x_2+mx_2=5$$

Given the midpoint is at origin, we have $x_1=-x_2$, which yields $m=\frac32$.