CBSE Class 10 Mathematics Coordinate Geometry Worksheet Set 01

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COORDINATE GEOMETRY
1 Prove that the points A(6, 2), B(2, 1), C(1, 5) and D(5, 6) are the vertices of a square.
 
2 Prove that the points A(2, -2 ), B(14, 10), C(11, 13) and D(-1, 1) are the vertices of a rectangle.
 
3 Prove that the points (7, 10),(- 2, 5) and (3, - 4) are the vertices of an isosceles right triangle.
 
4 Prove that the points (0, 0), (5, 5) and (-5, 5) are the vertices of an isosceles right triangle
 
5 Find the ratio in which the line segment joining the points A(3, - 3) and B(- 2, 7) is divided by x axis. Also find the co-ordinates of the point of division.
Ans (3/2 , 0)
 
6 Find the ratio in which the line segment joining the points A(-4, 5) and B(- 3, 7) is divided by y axis. Also find the co-ordinates of the point of division. (Ans: 4 : 3)
 
7 Find the area of the quadrilateral ABCD, the co-ordinates of whose vertices are A(5, -2), B(-3, -1), C(2, 1) & D (6, 0)
(Ans: 15 sq units)
 
8 Find the area of the quadrilateral ABCD, the co-ordinates of whose vertices are A(1, 0), B(5, 3), C(2, 7) & D (-2, 4)
(Ans: 25 sq units)
 
9 For what values of k are the points (8, 1), (3, -2k), and (k, -5) collinear?
(Ans 2,11/2)
 
10 Find the values of k so that the area of the triangle with vertices (1, - 1), (- 4, 2k) and (-k, -5) is 24 sq units.
(Ans: k = 3, -9/2)
 
11 For what values of k are the points (7, -2), (5, 1), and (3, 2k) collinear?
(Ans: k = 2)
 
12 Find the value(s) of k so that the area of the triangle with vertices (1, k), (4, -3) and (-9, 7) is 15 sq units.
(Ans: k = -3, 21/13)
 
13 Three consecutive vertices of a parallelogram are (-2, -1), (1, 0) and (4, 3). Find the fourth vertex.
(Ans: (1,2))
 
14 If (1, 2). (4, y), (x, 6) and (3, 5) are the vertices of a parallelogram taken in order, then find x and y.
(Ans: x = 6, y = 3)
 
15 Three consecutive vertices of a parallelogram are (2, -1), (3, 4) and (-2, 3). Find the fourth vertex.
(Ans: (-1,-2))
 
 
 
More MCQs for NCERT Class 10 Mathematics Coordinate Geometry....
 
 
1. The lines, x = 2 and y = 3 are
 
(A) parallel to each other

(B) perpendicular to each other

(C) neither parallel nor perpendicular to each other

(D) none of these
 
Answer : (B)
 

2. The lines, x = –2 and y = 3 intersect at the point ________.
(A) (-2,3) 
 
(B) (2,-3) 
 
(C) (3,-2) 
 
(D) (-3,2)
 
Answer :  (A)
 

3. The slope of the line joining the points (2, k – 3) and (4,-7) is 3. Find k.
(A) -10 
 
(B) -6 
 
(C) -2 
 
(D) 10
 
Answer : (A)  
 

4. The centre of a circle is C(2,-3) and one end of the diameter AB is A(3,5) . Find the coordinates of the other end B.
(A) (1,-11) 
 
(B) (5,2) 
 
(C) (1,8) 
 
(D) none of these
 
Answer :   (B)
 

5. The points on X-axis which are at a distance of 13 units from (-2,3) is ________.
(A) (0,0), (-2,-3) 
 
(B) (0,0), (-4,0) 
 
(C) (0,0), (2,3) 
 
(D) none of these
 
Answer : (B)  
 

6. The point P lying in the fourth quadrant which is at a distance of 4 units from X-axis and 3 units from Y-axis is__________.
(A) (4,-3) 
 
(B) (4,3) 
 
(C) (3,-4) 
 
(D) (-3,4)
 
Answer : (C) 
 

7. The points (a,b +c), (b,c +a) and (c,a + b)
(A) are collinear
 
(B) form a scalene triangle

(C) form an equilateral triangle 
 
(D) none of these
 
Answer : (A)  
 

8. Find λ , if the line 3x - λy +6 = 0 passes through the point (–3,4).
(A) 3/4

(B) -3 /4

(C) 4/3

(D) -4/3
 
Answer :  (B)
 

9. If A(-2,3) and B(2,3) are two vertices of △ABCand G(0, 0) is its centroid, then the coordinates of C are
(A) (0,-6) 
 
(B) (-4,0) 
 
(C) (4,0) 
 
(D) (0,6)
 
Answer : (A)  
 

10. Let △ABCbe a right angled triangle in which A(0, 2) and B(2, 0). Then the coordinates of C can be
(A) (0, 0)
 
(B) (2, 2) 
 
(C) either (A) or (B) 
 
(D) none of these
 
Answer : (C)  
 

11. Find the area of the triangle formed by the line 5x -3y +15 = 0with coordinate axes.
(A) 15cm2 
 
(B) 5 cm2 
 
(C) 8 cm2 
 
(D) 15/2cm 2
 
Answer : (D)  
 
 
12. The centre of a circle is C(2, k). If A(2, 1) and B(5, 2) are two points on its circumference, then the value of k is
(A) 6 
 
(B) 2 
 
(C) –6 
 
(D) –2
 
Answer : (A)  
 

13. The distance between the points (2k + 4, 5k) and (2k, –3 + 5k) in units is
(A) 1 
 
(B) 2 
 
(C) 4 
 
(D) 5
 
Answer : (D)  
 

14. The distance between the points (3k + 1, –3k) and (3k – 2, –4 –3k) (in units) is

(A) 3k 
 
(B) 5k 
 
(C) 5 
 
(D) 3
 
Answer : (C)  
 

15. If △ABCis a right angled triangle in which A(3, 0) and B(0, 5), then the coordinates of C can be
(A) (5, 3) 
 
(B) (3, 5) 
 
(C) (0, 0) 
 
(D) both (B) and (C)
 
Answer : (D) 
 

16. A triangle is formed by the lines x + y = 8,X-axis and Y-axis. Find its centroid.
(A) (8/3 ,8/3)

(B) (8, 8) 
 
(C) (4, 4) 
 
(D) (0, 0)
 
Answer : (A) 
 

17. The point which divides the line joining the points A(1, 2) and B(–1, 1) internally in the ratio 1 : 2 is _________.
(A) (1/3,5/3)

(B) (1/3,5/3)

(C) (–1, 5) 
 
(D) (1, 5)
 
Answer : (B) 
 

18. Find the area of the triangle formed by the line 3x -4y +12 = 0with the coordinate axes.
(A) 6 units2 
 
(B) 12 units2 
 
(C) 1 units2 
 
(D) 36 units2
 
Answer : (A) 
 

19. Find the equation of a line which divides the line segment joining the points (1, 1) and (2, 3) in the ratio 2 : 3 perpendicularly,
(A) 5x - 5y + 2 = 0 
 
(B) 5x +5y + 2 = 0

(C) x + 2y -5 = 0 
 
(D) x + 2y +7 = 0
 
Answer : (C)
 

20. The ratio in which the line joining (a + b, b + a) and (a – b, b – a) is divided by the point (a, b) is___________.
(A) b : a internally 
 
(B) 1 : 1 internally 
 
(C) a : b externally 
 
(D) 2 : 1 externally
 
Answer : (B)  
 

21. If the line (3x -8y+5)+a(5x -3y +10) = 0 is parallel to X-axis, then a is
(A) -8/3

(B)- 3/5

(C) –2 
 
(D) -1/2
 
Answer : (B)
  

22. Find the area of a triangle formed by the lines 4x - y-8 = 0,2x + y-10 = 0 and y = 0 (in sq units).
(A) 5 
 
(B) 6 
 
(C) 4 
 
(D) 3
 
Answer : (B)
 
 

23. Find the length of the longest side of the triangle formed by the line 3x + 4y =12with the coordinate axes.
(A) 9 
 
(B) 16
 
(C) 5
 
(D) 7
 
Answer : (C)
 
 

24. In what ratio does the line 4x +3y +13 = 0 divide the line segment joining the points (2, 1) and (1, 4)?
(A) 3 : 2 internally 

(B) 2 : 3 externally 

(C) 2 : 3 internally 

(D) 3 : 2 externally

Answer : (C)

 


25. If (5, 3), (4, 2) and (1, –2) are the mid points of sides of triangle ABC, then the area of △ABCis
(A) 2 sq. units 

(B) 3 sq. units 

(C) 1 sq. units 

(D) 4 sq. units

Answer : (A)

 


26. The ratio in which the line joining (1, 3) an (2, 7) is divided by 3x + y = 9 is
(A) 3 : 4 

(B) 2 : 4

(C) 1 : 2 

(D) 3 : 1

Answer : (A)

 


27. The point equidistant from vertices of a triangle is called
(A) circumcentre 

(B) incentre 

(C) orthocenter 

(D) none of these

Answer : (A)

 

28. The distance between the points (3, 4) and (6, –3) is.
(A) √58 

(B) √68 

(C) √78 

(D) √98

Answer : (A)

 

29. If A and B are (1, 4) and (5, 2) respectively, then the co-ordinates of P when AP/PB = 3/4 is
(A) 19/7 , 22 /7

(B) 20/7 , 21/7

(C) 21/7 , 22/7

(D) 21/7 , 23/7

Answer : (A)

 


30. If the coordinates of the mid-points of the sides of a triangle are (1, 2) (0, –1) and (2, –1). Then the sum of x coordinates of its vertices of the triangle is
(A) 3 

(B) 4 

(C) 5 

(D) 6

Answer : (A)

 

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Download CBSE Practice Material: Class 10 Mathematics Chapter 07 Coordinate Geometry

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