Question: What is the area of the parallelogram formed by the lines $y = mx, y = mx+1, y = nx, y = nx+1$?
a) $\frac{|m + n|}{(m - n)^2}$
b) $\frac{2}{|m + n|}$
c) $\frac{1}{|m + n|}$
d) $\frac{1}{|m - n|}$
I have no idea how to even approach this problem Please help?
Hint: First lets calculate all the points that form the parallelogram. Let us assume that $n\neq 0 \neq m$ The lines $y=mx$ and $y=nx$ intersect at $(0,0)$. The intersection of $y = mx+1$ and is at $(0,1)$ Then the intersection of $y=mx+1$ and $y=nx$ is at $(1/(n-m),n/(n-m)$ and because of the 'symmetry of the equations the intersection of $y=nx+1$ and $y=mx$ is at $(1/(m-n),m/(m-n))$
Here is a good answer onhow to calculate the area from the vertice points: Area of a parallelogram, vertices $(-1,-1), (4,1), (5,3), (10,5)$.