# Co Ordinate Geometry - Quantitative Aptitude Problems and Solutions

Various types of quadrialterals:-

```  A quadrilateral is
i) A rectangle if its opposite sides are equal and diagonals are equal.
ii) A parallelogram but not a rectangle, if its opposite sides are equal and the diagonals
are not equal.
iii) A square, if all sides are equal and diagonals are equal.
iv) Rhombus but not a square, if all sides are equal and diagonals are not equal```

1. 30.   The vertices of a ΔABC are A(-6, 18), B(12, 0) and C(9, −21). The centroid of ΔABC is:

 A.) (5, 1) B.) (5, -1) C.) (4, -1) D.) None of these

CENTROID OF A TRIANGLE

The point of intersection of all the medians of a triangle is called its centroid.

If A(x1, y1), B(x2, y2) and C(x3, y3) be the vertices of ΔABC,

then the co-ordinates of its centroid are [1/3(x1 + x2 + x3), 1/3(y1 + y1 + y3)]

= [1/3(-6+12+9), 1/3(18+0-21)]

= [15/3, -3/3]

= (5, -1)

2. 31.   The vertices of a quadrilateral ABCD are A(0, 0), B(3,3), C(3, 6) and D(0, 3). Then , ABCD is a

 A.) square B.) parallelogram C.) rectangle D.) rhombus

AB2 = (3-0)2 + (3-0)2 = 18

BC2 = (3-3)2 + (6-3)2 = 9

CD2 = (0-3)2 + (3-6)2 =18

AD2 = (0-0)2 + (3-0)2 = 9

AB = CD = √18 => 3√2,

BC = AD = √9

AC2 = (3-0)2 + (6-0)2 = 9 + 36 = 45

BD2 = (0-3)2 + (3-3)2 = 9 + 0 = 9

AC ≠ BD

ABCD is a parallelogram.

3. 32.  The points A(1, -3), B(13, 9), C(10, 12) and D(-2, 0) taken in order are the vertices of

 A.) square B.) rhombus C.) parallelogram D.) rectangle

AB2 = (13-1)2 + (9+3)2

= 122 + 122 = 288.

BC2 = (10-13)2 + (12-9)2

= -32 + 32 = 9+9 = 18

CD2 = (10+2)2 + (12-0)2

= 122 + 122 = 288

AD2 = (-2-1)2 + (0+3)2 = (9+9) =18

AB = CD and BC = AD

AC2 = (10-1)2 + (12+3)2

= 92 + 152 = 81 + 225 = 306.

BD2 = (-2-13)2 + (0-9)2

= 225 + 81 = 306

AC = BD

ABCD is a rectangle.

4. 33.   If for a line m = tanϑ < 0, then

 A.) ϑ is acute B.) ϑ is obtuse C.) ϑ = 90° D.) ϑ = 60°

m = tanϑ < 0 => is obtuse

5. 34.   If for a line m = tanϑ > 0, then

 A.) ϑ is acute B.) ϑ is obtuse C.) ϑ = 90° D.) ϑ = 60°

m = tanϑ < 0 => is acute

Quantitative Aptitude Topics

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