What type of quadrilateral is formed by connecting the points (0,0), (3x,b), (18x,b), and (15x,0)? How would I solve this?

Answer 1

Since x and b are supposed to be valid for any value, take x=b=2 (or any other number) and sketch the graph.
If you recognize any shape, then use the properties of the shape to do the general proof.

Example:
for x=b=2, the points become:
(0,0),(6,2),(36,2),(30,0)
A sketch shows that it is a parallelogram.
Now you will need to prove that the (general) quadrilateral is a parallelogram.
Examples:
- two pairs of parallel opposite sides
- two opposite sides are parallel and equal