List of top Quantitative Aptitude Questions on Coordinate Geometry

What is the area, in square units, of the triangle formed by the points \( (3, 2), (3, -6) \) and \( (5, 2) \)?

The point \((-2, 3)\) lies in which quadrant?

Find the distance between points (2, 3) and (5, 7).

A rectangle has a perimeter of 50 cm and an area of 150 cm². Find its length.

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).

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 $5x-6y=1$.

ABCD is a rectangle. Points \( P \) and \( Q \) lie on \( AD \) and \( AB \) respectively. If triangles \( PAQ, QBC, \) and \( PCD \) all have the same areas and \( BQ = 2 \), then \( AQ = \) ?

Find the area bounded by the curves $|x + y| = 1$, $|x| = 1$, $|y| = 1$.

ABCD is a rhombus with AC and BD intersecting at the origin. The equation of side AD is $x + y = 1$. What is the equation of BC?

From 5 points (4 vertices of a square + 1 intersection point of diagonals), how many triangles can be formed?

ABC is an equilateral triangle with AB = AC, and B is 2 km north of A. A person walks from B parallel to AC, stops when directly east of C (point D). Where is D with respect to A?

What is the total distance walked by the person (from B to D to E)?

A slab of ice 8 in × 11 in × 2 in is melted and recast into a cylinder of 8 in diameter. What is the length of the cylinder?