Rectangular Cartesian System Questions with Solutions

12 questions5 easy7 medium

The rectangular Cartesian coordinate system locates any point in a plane by its distances from two perpendicular axes, written as an ordered pair (x, y). It is the starting point for all of coordinate geometry. This topic covers quadrants, the distance formula, the section formula (internal and external division), the midpoint formula, the area of a triangle from its vertices, and collinearity of points. It also covers special points of a triangle such as the centroid, incentre and circumcentre, and the locus of a point. A useful check is that three points are collinear exactly when the area of the triangle they form is zero. Questions here are usually formula-based and can be solved quickly with careful sign handling. Practise the Cartesian coordinate system questions below, each with a step-by-step solution.

All Questions Easy Medium Hard

Q1.
A triangle has a vertex at (1, 2) and the midpoints of the two sides through it are (−1, 1) and (2, 3). Then the area of this triangle is
A. 1B. 2C. 3D. 4
easyAsked in NIMCET 2026View solution ›
Q2.
If $(4, - 3)$ and $(- 9, 7)$ are two vertices of a triangle and $(1, 4)$ is its centroid, then the area of the triangle is
A. $\frac{138}{2}$ B. $\frac{319}{2}$ C. $\frac{183}{2}$ D. $\frac{381}{2}$
easyAsked in NIMCET 2012View solution ›
Q3.
If the distance of $(x, y)$ from the origin is defined as $d (x, y) = ma x (∣ x ∣, ∣ y ∣)$ , then the locus of points where $d (x, y) = 1$ is:
A. a square of area 1 sq. unitB. a circle of radius 1C. a triangleD. a square of area 4 sq. units
easyAsked in NIMCET 2009View solution ›
Q4.
If $a, b, c$ are the roots of the equation $x^{3} - 3 p x^{2} + 3 q x - 1 = 0$ , then the centroid of the triangle with vertices $(a, \frac{1}{a})$ , $(b, \frac{1}{b})$ and $(c, \frac{1}{c})$ is the point
A. $(p, q)$ B. $(\frac{p}{3}, \frac{q}{3})$ C. $(p + q, p - q)$ D. $(3 p, 3 q)$
easyAsked in NIMCET 2008View solution ›
Q5.
If P(1, 2), Q(4, 6), R(5, 7) and S(a, b) are the vertices of a parallelogram PQRS, then
A. a = 2, b = 3B. a = 3, b = 4C. a = 2, b = 4D. a = 3, b = 5
easyAsked in NIMCET 2021View solution ›