The exercise is written as,
Find a point P upon the line r: -3x + 4y + 1 = 0, such as that the line which contains the segment OP (O: origin of coordinates) passes through the midpoint of the line segment AB, where A = (2,1) and B = (1,1).
I know how to find the cartesian equation of a line given two points, but I'm not sure if I need to do that for the exercise. I also know that the midpoint is the sum of the x and y coordinates of each point over two.
I also know that if the lines are perpendicular to each other, then the dot product is zero.
However I'm really unsure of how to find a point upon that line, or even if I'm looking in the right direction at the exercise.
Do you know how to compute the intersection of two lines ? If so, let $C$ be the mid of segment $[AB]$, i.e. $C=\frac{A+B}{2}$ and let $\rho$ be the line going through O and C (whose equation should not be too hard). Those two lines are the line described in the problem. Since lines intersect at one point at most and $P$ belongs to both, you can compute $P$ by computing the intersection between line $r$ and line $\rho$.