If P(1, 2), Q(4, 6), R(5, 7) and S(a, b) are the vertices of a parallelogram PQRS, then

Rectangular Cartesian System — Preparation

This question tests your understanding of Rectangular Cartesian System, a key topic in the Quantitative Aptitude section. The detailed solution above uses a step-by-step approach to show the reasoning, and where available, a shortcut that helps you solve similar questions in under 90 seconds during the actual exam.

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.