SOLUTION: In a rhombus ABCD, AB is parallel to the straight line {{{x-y=5}}} and BC is parallel to {{{7x-y=3}}}. If the diagonals of the rhombus intersect at the point (2, 1), find the equat

Question 1105882: In a rhombus ABCD, AB is parallel to the straight line and BC is parallel to . If the diagonals of the rhombus intersect at the point (2, 1), find the equations of the diagonals.
Answer by ikleyn(52814) (Show Source): You can put this solution on YOUR website!
.
It is NOT POSSIBLE to solve the problem (to get a solution) based on given data.

The given data is NOT SUFFICIENT to get a unique (a single) answer.

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Comment from student: Hello. This message is in response to question #1105882. First of all, thanks a lot for your time. I really appreciate it.
I was wondering why the problem didn't have sufficient data to get a unique answer, when suddenly I though
about a few things:
1. If we know the slopes of the sides of the rhombus, shouldn't we be able to calculate the slopes of the diagonals?
2. And, once we know the slopes of the diagonals, we also have their intersection point (that is, (2, 1)).
3. Combining them both, we'll have one slope and one point for each diagonal.
4. So can't we use the slope-point form of a line to get the eqation of each diagonal? I'm a bit confused over here.
I'll be grateful if you could help me with this. Thanks again. :)
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My responce. For a minute, imagine your rhombus on a plane with its sides parallel to the given lines.

Next imagine that you do translate your rhombus as the whole thing over the plane, by keeping its sides parallel to the given direction.

The intersection point of the diagonals will move with the rhombus, agree ?

It means that your problem DOES NOT HAVE a unique solution.

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