How to find the coordinates of vertices of the square

Question

The equations of two sides of a square are $y=3x-1$ and $x+3y-6=0$. If $(0,-1)$ is one vertex of the square find the coordinates of the other vertices.

I've graphed the parallel lines but not sure on how to get the coordiantes.

Answer 1

Hints:

Write the equations of the parallels to the given line passing through the given point. By intersecting the non-parallel lines, you will find other vertices. Use vector addition to find all vertices.

If it turns out that the intersection only gives you one new vertex, you can rotate the vector by 90° using $(u,v)\to(v,-u)$.

Answer 2

HINT :(in short)Use the prooerties of square ( All sides has equal length )

This is plot of your two lines

Find intersection of those two lines Now plot (0,-1) and draw lines parallel to $x+3y-6=0$ and passes through (0,-1).

Then, Find other two points using the properties of square ( All sides of square has same length).