Learn Problems on Coordinate Geometry and crack CAT Quantitative Apitude

Coordinate Geomtery offers quite a formulaic approach to finding solutions to a large number of problems asked in Quantitative Aptitude of CAT.In this article, we have tried to give you the flavour of the problems that are basic and some of the ones that look formidable when you first read the problem, but are actually very simple and logical to solve.

Example:

If (5, 1), (x, 7) and (3, -1) are 3 consecutive vertices of a square then x is equal to:

[1] - 3

[2] - 4

[3] 5

[4] 6

Solution:

For the vertices to form a square, we know that the length of each side of the square should be equal. Therefore,

This gives theside of the square,x = –3. Therefore, the correct option is [1].

Example:

Let g (x) = max(5 - x, x + 2). Then, the smallest possible value of g (x) is:

(1)    4.0

(2)    4.5

(3)    1.5

(4)    None of these

Solution:

Please note that we are required to find out the minimum value of g (x) , but the nature of the function g (x) is such that it will give the maximum out of the two values of (5 - x) or (x - 2) , whichever is higher.

If we graph the function,

y₁ = 5 - x

and y₂ = x = 2 , we get:

The intersection point P of the two lines is the point where,

It is clear from the graph that point is the point where the functiong(x) will produce the smallest value of . max(5 - x, x + 2).Therefore, the correct option is [4].

Example:

These questions are based on the data given below.

The following are two functions defined in the xy plane for any point (x, y) where x, y,a andb are positive.

Function 1: Rot (x, y) = (ax, y)

Function 2: Dec (x, y) = (x, by)

For a = 7, b = 3 Find the area of the quadrilateral whose vertices are (2, 3), Rot(2, 3), (5, 2) and Dec(5, 2).

[1] 12 sq. units

[2] 18 sq. units

[3] 24 sq. units

[4] 28 sq. units

Solution:

The given functions are:

Function 1: Rot (x, y) = (ax, y)

Function 2:  Dec (x, y) = (x, by)

We are given, a = 7 and b = 3

Therefore, Rot (x, y) = (ax, y) will give us: (14, 3)

and Dec (x, y) = (x, by) will give us: (5, 6)

The four vertices of the quadrilateral will now be: (2,3), (5,2), (14,3) and (5,6)

These are shown on the Cartesian plane in the figure below.

Therefore the correct option is [3]