CBSE Class 10 Coordinate geometry Sure Shot Questions Set C

CBSE Class 10 Coordinate geometry Sure Shot Questions Set C. There are many more useful educational material which the students can download in pdf format and use them for studies. Study material like concept maps, important and sure shot question banks, quick to learn flash cards, flow charts, mind maps, teacher notes, important formulas, past examinations question bank, important concepts taught by teachers. Students can download these useful educational material free and use them to get better marks in examinations.  Also refer to other worksheets for the same chapter and other subjects too. Use them for better understanding of the subjects.

1. Find the area of a triangle formed by the points A(5, 2), B(4, 7) and C(7, – 4).

2. Find the area of a triangle formed by the points A(1, –1), B(– 4, 6) and C(– 3, – 5).

3. Find the area of a triangle formed by the points A(2, 3), B(– 1, 0) and C(2, –4).

4. Find the area of a triangle formed by the points A(10, –6), B(2, 5) and C(– 1, 3).

5. Determine if the points (1, 5), (2, 3) and (– 2, – 11) are collinear.

6. Show that the points ( -3 /2, 3), (6, –2), (–3, 4) are collinear by using area of triangle.

7. By using area of triangle show that the points (a, b + c), (b, c + a) and (c, a + b) are collinear.

8. Find the value of k if the points A(8, 1), B(k, –4) and C(2, –5) are collinear.

9. Find the value of k if the points A(7, –2), B(5, 1) and C(3, k) are collinear.

10. If A(3, 2), B(–1, 0) and C(1, –12) are the vertices of a triangle and D is midpoint of BC, find the coordinates of the point D. Also find the areas of ΔABD and ΔACD. Hence verify that the median AD divides the triangle ABC into two triangles of equal areas.

11. Find the value of k if the points A(2, 3), B(4, k) and C(6, –3) are collinear.

12. If A(–5, 7), B(– 4, –5), C(–1, –6) and D(4, 5) are the vertices of a quadrilateral, find the area of the quadrilateral ABCD.

13. If A(2, 1), B(6, 0), C(5, –2) and D(–3, –1) are the vertices of a quadrilateral, find the area of the quadrilateral ABCD.

14. If A(–4, 5), B(0, 7), C(5, –5) and D(–4, –2) are the vertices of a quadrilateral, find the area of the quadrilateral ABCD.

15. If A(0, 0), B(6, 0), C(4, 3) and D(0, 3) are the vertices of a quadrilateral, find the area of the quadrilateral ABCD.

16. If A(–4, –2), B(–3, –5), C(3, –2) and D(2, 3) are the vertices of a quadrilateral, find the area of the quadrilateral ABCD.

17. Find the area of the triangle formed by joining the mid-points of the sides of the triangle whose vertices are (0, –1), (2, 1) and (0, 3). Find the ratio of this area to the area of the given triangle.

18. Find a relation between x and y if the points (x, y), (1, 2) and (7, 0) are collinear. 

19. If A(2, 1), B(–2, 3) and C(4, –3) are the vertices of a △ABC and D, E are the midpoints of the sides AB, AC respectively, find the coordinates of D and E. Prove that the area of △ABC is four times the area of △ADE.

20. If A(4, 4), B(3, –16) and C(3, –2) are the vertices of a △ABC and D, E, F are the midpoints of the sides BC, CA and AB respectively. Prove that the area of △ABC is four times the area of △DEF.

21. Find the point P on the x – axis which is equidistant from the points A(5, 4) and B(–2, 3). Also find the area of △PAB.

22. If P(x, y) is any point on the line joining the points A(a, 0) and B(0, b), then show that x/a + y/b =1 

23. If the vertices of a triangle are (1, k), (4, –3) and (–9, 7) and its area is 15 sq. units, find the value(s) of k.

24. Find the value of m for which the points with coordinates (3, 5), (m, 6) and 1/2 ,15/2 ) are collinear.

25. Find the value of k for which the points with coordinates (2, 5), (4, 6) and ,(k , 11/2) are collinear.

26. Find the point P on x-axis which is equidistant from A(–2, 5) and B(2, –3). Also find the area of △PAB.

27. Find the point P on x-axis which is equidistant from A(7, 6) and B(–3, 4). Also find the area of △PAB.

28. Find the point P on the x-axis which is equidistant from A(2, –5) and B(–2, 9). Also find the area of △PAB.

29. Find a point P on the y-axis which is equidistant from the points A(6, 5) and B(– 4, 3). Also find the area of △PAB.

30. Find a point P on the y-axis which is equidistant from the points A(5, 2) and B(– 4, 3). Also find the area of △PAB.

31. Find a point P on the y-axis which is equidistant from the points A(5, – 2) and B(– 3, 2). Also find the area of △PAB.

32. Find the value of k for which the area formed by the triangle with vertices A(k, 2k), (–2, 6) and C(3, 1) is 5 square units.

33. Find the value of k for which the area formed by the triangle with vertices A(1, 2), (–2, 3) and C(–3, k) is 11 square units.

34. Find the value of k for which the area formed by the triangle with vertices A(4, 4), (3, k) and C(3, –2) is 7 square units.

35. For what value of p are the points A(–3, 9), B(2, p) and C(4, –5) are collinear.

36. Prove that the area of triangle whose vertices are (t, t – 2), (t + 2, t + 2) and (t + 3, t) is independent of t.

37. For what value of k are the points (k, 2 – 2k), (–k + 1, 2k) and (–4 – k, 6 – 2k) are collinear.

38. Find the condition that the point (x, y) may lie on the line joining (3, 4) and (–5, –6).

39. If the coordinates of two points A and B are (3, 4) and (5, –2) respectively. Find the coordinates of any point P, if PA = PB and area of △PAB = 10 sq. units.

40. The coordinates of A, B, C are (6, 3), (–3, 5) and (4, –2) respectively and P is any point (x, y). Show that the ratio of the areas of triangles PBC and ABC is

41. If (x, y) be on the line joining the two points (1, –3) and (–4, 2), prove that x + y + 2 = 0.

42. Prove that the points (a, b), (x, y) and (a – x, b – y) are collinear if ay = bx.

43. Four points A(6, 3), B(–3, 5), C(4, –2) and D(x, 3x) are given in such a way that DBC /ABC = 1/2 find the value of x.

44. If three points (a, b), (c, d) and (e, f) are collinear, prove that d-f/ce +f-b/ea + b-d /ac =0

45. The area of triangle is 5 sq. units. Two of its vertices are (2, 1) and (3, –2). The third vertex lie on y = x + 3. Find the third vertex.

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