List of top Quantitative Aptitude Questions on Coordinate Geometry asked in XAT

Determine the value(s) of “a” for which the point $(a, a^2)$ lies inside the triangle formed by the lines: $2x+3y=1$, $x+2y=3$ and $5x-6y=1$.

OABC is a square where O is the origin and AB = 1. Consider the set of points S = (x_i, y_i) in the square such that x_i + y_i ≤ 1.

Let P(x₁, y₁) and Q(x₂, y₂) be two such points. Two operations addition (+) and multiplication (·) on S are defined as:

P + Q = (x₁ + x₂ − x₁x₂, y₁y₂)

P · Q = (x₁x₂,   y₁ + y₂ − y₁y₂)

Let A₁, A₂, …, A_n be the points on the straight line y = px + q. The coordinates of A_k is (X_k, Y_k), where k = 1, 2, …, n such that X₁, X₂, …, X_n are in arithmetic progression. The coordinates of A₂ is (2, −2) and A₂₄ is (68, 31).