List of top Quantitative Ability and Data Interpretation Questions on Coordinate Geometry asked in XAT

Given five points A = (7, 4), B = (-10, 0), C = (-10, 3), D = (0, 10) and E = (7, 7). Every second, all the points move by halving their abscissas (x-coordinates) and doubling their ordinates (y-coordinates). This process continues for 500 years. After 500 years, which two points are closest?

The coordinates of P and Q are (0, 4) and (a, 6), respectively, where a is a non-zero integer. R is the midpoint of PQ. The perpendicular bisector of PQ cuts the X-axis at the point S(b, 0). For how many integer values of a is b also an integer?

For which value of non-negative 'a' will the system \(x^2 - y^2 = 0\), \((x-a)^2 + y^2 = 1\) have exactly three real solutions?

Triangle ABC has vertices A(0, 0), B(0, 6) and C(9, 0). The points P and Q lie on side AC such that AP = PQ = QC. Similarly, the points R and S lie on side AB such that AR = RS = SB. If the line segments PB and RC intersect at X, then the slope of the line AX is:

47. Which equation can be graphically represented as follows?

Directions: Each of the following questions is followed by two statements. As the answer, mark (1) if the question can be answered with the help of statement I alone, mark (2) if the question can be answered with the help of statement II alone, mark (3) if both statement I and statement II together are needed to answer the question, and mark (4) if the question cannot be answered even with the help of both the statements.

Is line MN perpendicular to the X-axis?
I. M = (5, 12)
II. N lies on the X-axis at a distance of 5 units from the origin.