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Class 10 Maths Important Questions(3 Marks questions) for Coordinate Geometry





Given below are the Class 10 Maths Important Questions(3 Marks questions) for Coordinate Geometry
a) Concepts questions
b) Calculation problems
c) Multiple choice questions
d) Long answer questions
e) Fill in the blank's
  1. Find the centre of the circle passing through (6, -6), (3, -7) and (3, 3)
  2. Two opposite vertices of a square are (-1, 2) and (3, 2). Find thee co-ordinates of other two vertices.
  3. Prove that the points (3, 0), (4, 5), (-1, 4) and (-2, -1), taken in order, form a rhombus. Also, find its area.
  4. Find a point on y – axis which is equidistant from the points (5, -2) and (-3, 2).
  5. Find a relation between a and b such that the point (a, b) is equidistant from the points (3, 6) and (-3, 4).
  6. If the coordinates of the mid points of the sides of a triangle are (1, 2), (0, -1) and (2, -1). Find the coordinates of its vertices.
  7. The coordinates of one end point of a diameter of a circle are (4, -1) and the co-ordinates of the centre of the circle are (1, -3). Find the co- ordinates of the other end of the diameter.
  8. If A (5, -1), B (-3, -2) and C (-1, 8) are the varieties of triangle ABC, find the length of median through A and the co- ordinates of the centroid.
  9. If the mid- point of the line joining (3, 4) and (z, 7) is (x, y) and 2x + 2y + 1 = 0 find the value of z.
  10. Find the ratio in which the line segment joining (-2, -3) and (5, 6) is divided by (i) x – axis (ii) y –axis. Also, find the co- ordinates of the point of division in each case.
  11. Prove that (4, 3), (6, 4), (5, 6) and (3, 5) are the angular points of a square.
  12. Three vertices of a parallelogram are (a +b, a – b), (2a + b, 2a – b), (a – b, a + b).Find the fourth vertex.
  13. If two vertices of a parallelogram are (3, 2), (-1, 0) and the diagonals cut at (2, -5), find the other vertices of the parallelogram.
  14. Find the lengths of the medians of a Δ ABC having vertices at A (0, -1), B (2, 1) and C (0, 3).
  15. Find the lengths of the medians of a Δ A (5, 1), B (1, 5) and C (-3, -1).
  16. Find the co- ordinates of the points which divide the line segment joining the points (-4, 0) and (0, 6) in four equal parts.
  17. Show that following points are vertices of a rectangle:
           (a) (2 , –2) , ( 8, 4) , ( 5, 7 ) , (– 1, 1)
           (b)(–4 , –1) , (–2 , 4) , ( 4, 0 ) , ( 2, 3 )
    18.     If centre of circle passing through (a,–8), (b,–9) and (2,1) is (2,–4), find the value of a and b.
Answer
1. (3, -2)
2. (1, 0) and (1, 4)
3. Area = 24 sq. units
4. (0, -2)
5. 3a + b = 5
6. (1, -4), (3, 2), (-1, 2)
7. Co- ordinates are (-2, -5)
 8. Median = √65 units, co- ordinate = [ 1/3,5/3 ]
 9.  z =-15
10 (i) 1 : 2; [1/3,0]
     (ii) 2 : 5; [ 0, -3/7 ]
12. (-b, b)
13. (1, -12), (5, -10)
14. AD = 10 units, BE = 2units, CF = 10 units
15. AD = 37 units, BE = 5 units, CF = 2 13 units
16. (-3, 1.5), (-2, 3), (-1, 4.5)


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