Toughie from MGMAT - looking for creative and different approaches to approach this problem.
In the rectangular coordinate system, are the points (a, b) and (c, d) equidistant from the origin?
(1) a/b = c/d
(2)sqrt(a^2)+sqrt(b^2) =sqrt(c^2) +sqrt(d^2)
OA is C.
I have seen a couple of nice approaches on number plugging, but just checking if there are any other innovative ideas to think conceptually on this. I myself tried algebra...then tried to switch mid-way to plugging and messed it on time...
So pointers on CONCEPT, GUESSING, TAKEAWAYS on how to recognize what approach to adopt,,... all welcome.
The question is asking about the distance from the origin. Statement 1
says only about the ratio (a/b = c/d) of the coordinates of the points (a, b) and (c, d).
If a = 3 and b = 1, a/b = 3.
c/d could be three in many ways...That's clearly not sufficient..Statement 2
sqrt(a^2)+sqrt(b^2) =sqrt(c^2) +sqrt(d^2)
i.e. a+b = c+d.
This is possible in many ways. This is also not sufficient..Statements 1 and 2
: I wonder how to solve algebraically!
a/b = c/d ........................(i)
a + b = c + d ....................(ii)
suppose a/b = c/d = 3
a = 3b
c = 3d
3b + b = 3d + d ....................(iii)
4b = 4d
b = d
If b = d, a has to be equal to c. If so, coordinates points (a, b) and (c, d) are in equi-distance from the origin...