jainrahul1985 wrote: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 C

We can apply the Distance formula to find the distance of points (a, b) and (c, d) from origin, (0, 0).
So, distance of (a, b) from (0, 0) = √(a² + b²)
Distance of (c, d) from (0, 0) = √(c² + d²)

Question is: Is √(a² + b²) = √(c² + d²) or is a² + b² = c² + d²?

(1) a/b = c/d implies a/b = ck/dk (for any constant k, which is not equal to zero)
Then a = kc and b = kd
This clearly implies that (1) is NOT SUFFICIENT.

(2) √a² + √b² = √c² + √d² implies |a| + |b| = |c| + |d|
Again, (2) is NOT SUFFICIENT.

Combining (1) and (2), |kc| + |kd| = |c| + |d| implies |k|[|c| + |d|] = |c| + |d| or |k| = 1
Hence |a| = |c| and |b| = |d| implies a² + b² = c² + d²
So, combining the two statements is SUFFICIENT to answer the question.

The correct answer is C.