I have a question that I've started at school but had couldn't figure out what to do or where to start. Sorry, I don't have the question written down, just the image. Help is much appreciated.
In the diagram to the right, point $P$ lies on the line $\displaystyle y = \frac{3}{2}x$ and is one vertex of square $PQRS$. Point $R$ has coordinates $(5,0)$.
a. Find the coordinates of point $P$.
b. If point $R$ lies on line $l$, and line $I$ divides quadrilateral $PQRS$ into two regions of equal area, find the equation for line $l$.
Hint: The first big step to solving this problem is to figure out the $x$ and $y$ coordinate of $P$. Notice that there are two distinct constraints on $P$: it must lie on the line $y=\frac32x$, and it must be the corner of a square. For me, these problems are easier to think about if they are written entirely in equations. So my advice would be to figure out "what does it mean to be on the corner of that square?"
Keep in mind that you already know the coordinate of one corner, and you also know a few things about squares :)
For the second part, you should notice that it only takes two points to determine a line. If you choose a second point at random, this will be a rather difficult problem. So my advice would be to figure out "what is a good choice of a second point which will give more information?"