RRB NTPC - Co Ordinate Geometry - Problems and Solutions

1.

If the A(2, 3), B(5, k), and C(6, 7) are collinear, then k = ? 

   A.) 11
   B.) 12
   C.) 18
   D.) 6

Answer: Option 'D'

x1 = 2, x2 = 5, x3 = 6 and y1 = 3, y2 = k, y3 = 7 
Now Δ = 0 <=> 2(k - 7) + 5(7 - 3) + 6(3 - k) = 0 
      <=> 1/2 [2 (k-7) + 5(4) + 6(3-k)] = 0 
      <=> 2k - 14 + 20 + 18 - 6k = 0 
      <=> 24 - 4k = 0 
      <=> 4k = 24 
      <=> k = 6.

2.

The distance between the points A(5, -7) and B(2, 3) is:

   A.) 109
   B.) 5√7
   C.) √109
   D.) None of these

Answer: Option ''

AB2 = (2 - 5)2 + (3 + 7)2 
=> (-3)2 + (10)2 
=> 9 + 100 => √109

3.

The points A(0, 6), B(-5, 3) and C(3, 1) are the vertices of a triangle which is ? 

   A.) equilateral
   B.) right angled
   C.) isosceles
   D.) scalene

Answer: Option 'C'

AB2= (-5 - 0)2 + (-3 - 0)2 = 16 + 9 = 25 
BC2 = (3 + 5)2 + (1-3)2 = 82 + (-2)2 = 64 + 4 = 68 
AC2 = (3 - 0)2 + (1 - 6)2 = 9 + 25 = 34. 
AB = AC. ==> ΔABC is isosceles.

4.

A is a point on y-axis at a distance of 5 units from x-axis lying below x-axis. The co-ordinates of A are:

   A.) (5, 0)
   B.) (-5, 0)
   C.) (0, 5)
   D.) (0, -5)

Answer: Option 'D'

The co-ordinates of A are A(0, -5)

5.

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

Answer: Option 'B'

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 + y2 + y3)]
= [1/3(-6+12+9), 1/3(18+0-21)] 
= [15/3, -3/3] 
= (5, -1)

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