NTSE Mathematics Coordinate Geometry MCQs

Question: If the distance between the points (a, 2) and (3, 4) be 8 then a =

• a) 2 + 3√15  
• b) 2 - 3√15
• c) 2 ± 3√15
• d) 3 ± 2√15   

Answer: 3 ± 2√15   

Question: If the middle points of the sides of a triangle be (-2, 3), (4, -3) and (4, 5), then centroid of triangle is

• a)

  

• b)

  

• c)

  

• d)

  

Answer:

Question: If two opposite vertices of a squares are (5, 4) and (1, 6), then the coordinates of its remaining two vertices is

• a) (-2, 2) & (5, 3)
• b) (8, -3) (-2, 1)
• c) (8, 6) & (3, 5)
• d) (1, -3) & (2, 5)

Answer: (8, -3) (-2, 1)

Question: The point (11, 10) divides the line segment joining the points (5, -2) and (9, 6) in the ratio :

• a) 1 : 3 internally
• b) 1 : 3 externally
• c) 3 : 1 internally
• d) 3 : 1 externally

Answer: 3 : 1 externally

Question: The orthocenter of the triangle ABC is ‘B’ and the circumventer is ‘S’ (a, b). If A is the origin then the co-ordinates of C are :

• a) (2a, 2b)
• b)

  

• c)

  

• d) None of these

Answer: (2a, 2b)

Question: Value of m for which the point P (m, 6) divides the join of A (-4, 3) and B (2, 8) is

• a)

  

• b)

  

• c) -2
• d) None of these

Answer:

Question:  Four points A (6, 3), B(-3 ,5), C(4, -2) and D(x, 3x) are given in such a way that

then the value of x is

• a)

  

• b)

  

• c)

  

• d) None of these

Answer:

Question: In the points (k, 2 - 2k), (1 - k, 2k) and (- k - 4, 6 - 2k) be collinear, the possible values of k are

• a) -1/2
• b) 1/2
• c) 1
• d) -1

Answer: -1

Question: If A(-2, -1), B(a1 0), C(4, b) and D(1, 2) are the vertices of a parallelogram, Then the value of a and b is

• a) a - 2, b = 3
• b) a = 1, b = 2
• c) a = 3, b = 1
• d) a = 1, b = 3

Answer: a = 1, b = 3

Question: Orthocenter of triangle with vertices (0, 0), (4, 0) is

• a)

  

• b) (3, 12)
• c)

  

• d) (3, 9)

Answer:

More Questions.....................

Question: The image of the point P(-1, 2) in the line mirror 2x - 3y + 4 = 0 is

• a) (3, 2)
• b)

  

• c)

  

• d) (-5, 14)

Answer:

Question: The area bounded by the curves

• a) 1
• b) 2
• c)

  2√2    

• d) 4

Answer: 2

Question: Two opposite vertices of a rectangle are (1, 3) and (5, 1). If the other two vertices of the rectangle lie on the line y - x + λ = 0 then λ=

• a) -1
• b) 2
• c) 1
• d) None of these

Answer: 1

Question: The area of triangle formed by the lines x = 0, y = 0 and 

• a) ab
• b)

  

• c) 2ab
• d)

  

Answer:

Question: The equation of the altitude of the ABC whose vertices are A(-4, 2); B(6, 5) and C(1, -4) can be

• a) 10x + 3y + 2 = 0
• b) 5x + 9y + 2 = 0
• c) 6x + 5y = 0
• d) 5x - 6y = 0

Answer: 6x + 5y = 0

Question: The points on the line x + y = 4 which lie at a unit distance from the line 4x + 3y = 10, are

• a) (3, 1)
• b) (7, 11)
• c) (-7, 11)
• d) (1, 3)

Answer: (-7, 11)

Question: The incentre of the triangle with vertices (1,√3), (0, 0) and (2, 0) is

• a)

  

• b)

  

• c)

  

• d)

  

Answer:

Question: If A (-2,1), B(2,3) and C(-2, -4) are three points, then the angle between BA and BC is

• a)

  

• b)

  

• c)

  

• d)

  

Answer:

Question: Given the points A (0, 4) and B(0, -4), the equation of the locus of the point P (x, y)

• a) 9x2 - 7y2 + 63 = 0
• b) 9x2 - 7y2 - 63 = 0
• c) 7x2 - 9u2 + 63 = 0 
• d) 7x2 - 9y2 - 63 =0

Answer: 9x2 - 7y2 + 63 = 0

Question: If the distance between the points (3, k) and (4, 1) is  √10 then the value of k is

• a) 4 or 2
• b)

  

• c) -4 or 2
• d) 4 or -2

Answer: 4 or -2

Question: The point on the y - axis which is equidistant from A(-5, -2) and B(3, 2) is

• a) (0, -2)
• b) (0, 2)
• c) (-2, 0)
• d) (0, -4)

Answer: (0, -2)

Question: The vertices of a triangle are (-2, 0), (2, 3) and (1, -3), then the type of the triangle is

• a) Right triangle
• b) Equilateral
• c) Isosceles
• d) Scalene

Answer: Scalene

Question: The points which are not col linear are

• a) (0, 1), (8, 3) and (6, 7)
• b) (4, 3), (5, 1) and (1, 9)
• c) (2, 5), (-1, 2) and (4, 7)
• d) (-3, 2), (1, -2) and (9, -10)

Answer: (0, 1), (8, 3) and (6, 7)

Question: The coordinates of the point which divides the line segment joining the points (-7, 4) and (-6, -5) internally in the ratio 7 : 2 is

• a)

  

• b)

  

• c)

  

• d)

  

Answer:

Question: If the coordinates of the centroid of a triangle are (1, 3) and two of its vertices are (-7, 6) and (8, 5), then the third vertex of the triangle is

• a)

  

• b)

  

• c) (2, -2)
• d) (-2, 2)

Answer: (2, -2)

Question: The area of the triangle whose vertices are (a,a), (a + 1, a + 1) and (a + 2, a) is

• a) a3 
• b) 1
• c) 2a
• d) 2^1/2

Answer: a3 

Question: The ratio in which the line segment joining (3, 4) and (-2, -1) is divided by the x-axis is

• a) 3 : 2
• b) 4 : 1
• c) 4 : 3
• d) None of these

Answer: 4 : 1

Question: The points on the line x + y = 4 which lie at a unit distance from the line 4x + 3y = 10, are

• a) (3, 1)
• b) (7, 11)
• c) (-7, 11)
• d) (1, 3)

Answer: (-7, 11)

Question: The point on the y - axis which is equidistant from A(-5, -2) and B(3, 2) is

• a) (0, -2)
• b) (0, 2)
• c) (-2, 0)
• d) (0, -4)

Answer: (0, -2)

Question: The point (11, 10) divides the line segment joining the points (5, -2) and (9, 6) in the ratio :

• a) 1 : 3 internally
• b) 1 : 3 externally
• c) 3 : 1 internally
• d) 3 : 1 externally

Answer: 3 : 1 externally