Test 07 || Class 10th Maths || Ch. 07 Co-ordinate Geometry ( निर्देशांक ज्यामिति) (SIQ) 1

Some important sums of 

Test 07 || Class 10th Maths || Ch. 07 Co-ordinate Geometry 1

( निर्देशांक ज्यामिति)

1. Find the value of x if the distance between the points (x, - 1) and (3, 2) is 5.

यदि दो बिंदु (x, - 1) और (3, 2) के बीच की दूरी 5 हो तो x का मान ज्ञात करो।

2. Find the co-ordinate of a triangle ABC in which A (x, y), B (3,-5), C(- 7, 4) and centroid are G (2, - 1).

 त्रिभुज ABC के शीर्ष A (x, y) के निर्देशांक ज्ञात करो ज्ञात करो। जिनमें  B (3,-5), C(- 7, 4)   तथा G(- 7, 4) के निर्देशांक निम्न है।

3. If the point P(x, y) is equidistance from the point A (5, 1) and B (- 1, 5) prove that 3x= 2y.

यदि बिंदु P(x, y)  बिंदुओं A (5, 1) और B (- 1, 5) से समदूरस्थ हो तो सिद्ध करो कि 3x= 2y.

4 If the point (x, y) is equidistant from the point (a + b, b - a) and (a - b, a + b) prove that bx = a y.

यदि बिंदु (x, y)  बिंदुओं (a + b, b - a) और (a - b, a + b) से समदूरस्थ हो तो सिद्ध करो कि bx = ay.

5. If the distance of P ( x, y)  from the points A (3, 6) and B( - 3, 4) are equal, prove that 3x + y = 25.

यदि बिंदु P(x, y) बिंदुओं A (3, 6) और B( - 3, 4) से समदूरस्थ हो तो सिद्ध करो कि 3x + y = 25.

6. If A(4, - 8), B (3, 6) and C (5, - 4) are the vertices of a triangle ABC, D is the midpoint of BC and P is a point on a line such that AP /PD =  2, find the coordinates of P.

7. The coordinates of the midpoint of the line joining the points to (2p + 2, 3) and (4, 2q + 1) are (2p, 2q). Find the values of p and q.

8. A ( - 4, - 2), B (- 3, - 5) , C(3, - 2) and D (2, k) are the vertices of the quadrilateral ABCD. Find the value of k if the area of the quadrilateral is 28 square units.

9. The coordinates of the vertices of triangle ABC are A (4, 1),  B (- 3, 2) and C (0, k). Given that the area of triangle ABC is 12 unit square, find the value of k.

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

11. The coordinates of the midpoint of the line joining the points to (2p + 1, 4) and (5, q - 1) are (2p, q). Find the values of p and q.

12. Three consecutive vertex of the parallelogram ABCD are A (1, 2,), B (1, 0) and C (4, 0) then find the coordinates of the fourth vertex D

13. The line segment joining the points P (3, 3) and Q (6, - 6) is trisected at the point A and B such that A is nearer to P. If A lies on the line given by 2x + y + 1=0, find the value of k.

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

15. Determine the ratio in which the line 3x + 4y - 9 = 0 divides the line segment joining the points (1, 3) and (2, 7).

16. Let the opposite angular points of a square be (3, 4) and (1, - 1), find the coordinates of the remaining angular points.

17. The midpoints of the sides of the triangle are (3, 4), (4, 1) and (2, 0), find the coordinates of the vertex of the triangle.

18. If two vertices of an equilateral triangles are (0, 0) and (3, root 3), find the third vertex.

19. If the coordinates of the midpoints of the sides of a triangle are (1, 1), (2, - 3) and (3, 4), find its centroid.

20. Find the coordinates of the point equidistant from the points A (1, 2),  B (3, - 4) and C (5, - 6).

21. In which ratio the line 3x + y - 9 = 0 divides the line joining the points (1, 3) and (2, 7) internally.

22. In which ratio the line 2x +3 y = 10 divides the line joining the points (1, 2) and (2, 3) internally.                                               [2:3]

23. If the distance between the points (x, - 1) and (3, 2) is 5 then find the value of x.

                                                               [7, - 1]

24. If the three vertices of a parallelogram taken in order are (- 1, 0), (3, 1) and (2, 2) respectively find the coordinates of the fourth vertex.                        [ - 2, 1]

25. Two vertices of a triangle are (3, - 5) and (- 7, 4). if its centroid is (2, - 1) then find the third vertex.                                [ 10, - 2 ]

26. If the points P (1, 2), B (0, 0) and C (a, b) are collinear then show that 2a = b.

27. Let AB be the diameter of a circle whose centre is (2, - 3) and B (1, 4) then find the coordinates of A.

1. If the area of the triangle with vertex is (x, 3), (4, 4) and (3, 5) is 4 square unit find the value of x.

2. if x = a y =  b is the solution of the pair of the equation x minus y equal to 2 and X + y equal to 4 find the value of a and b.

3. find the linear relation between the x and y such that p (x, y) is equidistant from the points A (1, 4) and B ( - 1, 2).