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COORDINATE SYSTEM 

Objective Type Questions

1. The vertices of a triangle are (2, 1), (5, 2) and (3, 4) then circumcenter of the triangle
A:  

 

2. The co-ordinates of base BC of an isosceles triangle ABC are given by B(1, 3) and
     C (-2, 7). Which of the following points can be the possible coordinates of the vertex A?
A:  

 

3. 'P' and 'Q' are points on the line joining A(-2, 5) and B(3, 1) such that AP = PQ = QB, then the mid point of PQ is
A:  

 

4. If distance between (a, 2) and (3, 4) is 8 then a =
A:  

 

5. The coordinates of incentre and centroid of the triangle whose vertices are (-36, 7), (20, 7), (0, -8)
A:  (-1, 0)

 

6. If "G" be the centroid of a triangle ABC and "O" be any other point, then 
A:  3

 

7. In a ∆ ABC, if 'O' is mid point of 'BC', then  
A:  2

 

8. The locus of a point P(x, y) moves such that the sum of its distances from two fixed points (ae, 0) and (-ae, 0) is always 2a, is
A:  

 

9. The ends of a rod of length "l" move on two mutually perpendicular lines. The locus of the point on the rod which divides it in ratio 1 : 2 is
A:  

 

10. If  and (p, q) are the co-ordinates of circumcenter, centroid and orthocentre of a trinagle, then 
A:  2(α + β)

 

11. If P, Q, R divides the sides of the triangle ABC in the same ratio, then which of the following coincide for the triangles ABC, PQR?
A:  Centroid

 

12. If P(1, 2), Q(4, 6), R(5, 7) and S(a, b) are the vertices of a parallelogram PQRS, then
A:  a = 2, b = 3

 

13. If the vertices P, Q, R of a trinagle PQR are rational points. Which of the following points of the triangle PQR is (are) always rational points?
A) Centroid
B) Orthocentre
C) Circumcentre 
A:  All of these

 

14. If P be any point in the plane of square ABCD, then PA2 + PB2 =
A:  PC2 + PD2

 

15. If the point (x, y) is equidistant from the points (a + b, b - a) and (a - b, a + b), then the value of  
A:  

 

16. The equation of the locus of a point which moves so that the sum of their distances from (3, 0) and (-3, 0) is less than 9 is
A:  20x2 + 36y2 < 405

 

17. The locus of a point whose co-ordinates are given by x = t + t2 and y = 2t + 1 (where "t" is variable) is
A:  y2 = 4x + 1

 

18. The locus of the point of intersection of the lines x cos α + y sin α = a and x sin α - y cos α = b (where "α" is variable) is
A:  x2 + y2 = a2 + b2

 

19. A and B are fixed points, the vertex 'C' of ∆ABC moves such that cot A + cot B = constant. The locus of C is a straight line which is
A:  parallel to AB

 

20. If the sum of the distances of a point from two perpendicular lines in the plane is "1", then its locus is
A:  a straight line


21. If the distance of any point P(x, y) from the origin is defined as   then the locus of "P" is
A:  a straight line

 

22. If A(cos α, sin α), B(sin α, −cos α), C(1, 2) are the vertices of a ∆ ABC (where α is variable), then locus of centroid is
A:  3(x2 + y2) − 2x − 4y + 1 = 0

 

23. Let A(2, −3) and B(−2, 1) be the vertices of a triangle ABC. If the centroid of the triangle moves on the line 2x + 3y = 1, then the locus of the vertex 'C' is
 

A:  2x + 3y = 9
 

24. If the origin is shifted to the point (1, -2) without rotation, then the equation x2 + y2 − 4x − 4y becomes
A:  2x2 + y2 = 6

 

25. To what point the origin is to be shifted so that the equation y+ 4y + 8x − 2 = 0 will not contain term in "y" and the constant term?
A:  

 

26. Through what angle should the axes be rotated so that the equation 9x2 − 2xy + 7y2 = 10 may be changed to 3x2 + 5y2 = 5?
A:  60°

 

27. If the axes be turned through an angle tan−1 (2), what does the equation 4xy − 3x2 = a2 become
A:  x2 − 4y2 = a2

 

28. If (x, y) and (X, Y) be the coordinates of the same point referred to two sets of rectangular axes with the same origin. If ax + by becomes pX + qY where a, b are independent of x, y then a2 + b2 =
A:  p2 + q2

 

29. What does the equation (x − a)2 + (y − b)2 = r2 become when the axes are transferred to parallel axes through the point (a − c, b)?
A:  x2 + y2 − 2cx = r2 − c2

 

30. If by rotating the coordinate axes without translating the origin, the expression a1x2 + 2h1xy + b1y2 becomes a2x2 + 2h2xy + b2y2, then which of the following is wrong?
A:  (a1b2 + a2b1)2 = h12 + h22

 

31. The point (4, 1) undergoes the following transformation successively.
    (i) Reflection about the line y = x
    (ii) Transformation through a distance 2 units along the positive direction of X−axis
    (iii) Rotation through an angle Π/4 about the origin in anti clockwise direction
Final position of the point is given by coordinates is
A:  

 

32. A(2, 1), B(3, −7) are two points. C is any point on the line 3x − 2y = 1, then locus of point "D" such that ABCD is a parallelogram
A:  3x − 2y + 18 = 0

 

33. The point to which the origin is to be shifted so that the point (3, 0) may change to (2, −3) is
A:  (1, 3)

 

34. Matrix Matching


A:  (i) q (ii) r (iii) p

 

35.

A:  (i) q (ii) s (iii) r (iv) p

Posted Date : 19-02-2021

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