Class 10 Mathematics Solutions English Medium

Assignment Chapter - 7

Co-ordinate Geometory

Questions For Practice : 

3 Marks Questions: 

Q1.  Show that the points A (2, -2), B (14, 10), C (11, 13) and D (-1, 1) are

        the vertices of a rectangle.

Q2.  Determine the ratio in which the points (6, a) divides the join of

        A (-3, -1) and B (-8, 9). Also find the value of “a”.

Q3.  Find the point on the x-axis which is equidistant from the points (-2, 5)

        and (2, -3).find the coordinates of a point which divides internally the

        line segment joining the points (-3,-4) and (-8, 7) in the ratio of 7:5.

Q4.  Find the value of k for which the points (2, 5), (k, 11/2) and (4, 6) are

        collinear.

Q5.  Find the lengths of the median of the triangle whose vertices are

        (1,-1), (0, 4) and (-5,3) .

Q6.  Find the co-ordinates of the points of trisection of the line segment

        joining the points (3, -3) and (6, 9).

Q7.  The center of a circle of radius 13 units is the point (3, 6). P (7, 9) is

        a point inside the circle. APB is a chord of the circle such that

        AP = PB. Calculate the length of AB.

Q8.  The co-ordinates of the mid-point of the line joining the points (3p, 4)

        and (-2, 2q) are (5, p). Find the values of p and q.     

Q9.   If ‘a’ is the length of one of the sides of an equilateral triangle ABC

         base BC lies on x-axis and vertex B is at the origin, find the

         coordinates of the vertices of the triangle ABC.

Q10. The coordinates of the mid-point of the line joining the points

          (2p+1, 4) and (5, q – 1) are (2p, q). Find the value of p and q.

Q11. Find the value of K for which the points with coordinates (3, 2), (4, K)

         and (5, 3) are collinear.

Q12.  A is a point on the y-axis whose ordinate is 5 and B is the point

          (-3, 1). Calculate the length of AB.

Q13.  The distance between A (1, 3) and B(x, 7) is 5. Find the possible

           values of x

Q14. Show that the points (3, 3), (9, 0) and (12, 21) are the vertices of a

          right angled triangle. 

Q15.  The center of a circle is (1, -2) and one end of a diameter is (-3, 2),

          find the co-ordinates of the other end.

Q16.   Find the area of the quadrilateral whose vertices , taken in order

           are (-6,-2), (-3,-5) ,(4,-2) and (2,4)

Q17.   Find area of the square whose points are A(5,6) B( 1,5) C(2,1) 

           D( 6,2).

Q18.   Determine the ratio in which the points P (m, 6) divides the join of

           A (-4, 3) and B (2, 8). Also find the value of m.

Q19.   Find the value of p for which the points (-1, 3), (2, p) and (5,-1)

           are collinear.

Q20.   Calculate the ratio in which the line joining A (6, 5) and B (4,-3) is

           divided by the line y=2. Also find the point of division.

Q21.   If the points (x,y) is equidistant from the points (2,1) and (1,-2).

           Show that x+3y=0.

Q22.   Show that the points (1, 1), (-1,-1) and (  form an isosceles triangle.

Q23.   Find the coordinates of third side of the triangle if its two vertices

           are (-1, 4) and (5, 2) and mid point of one side is (0, 3).

Q24.   Find area of triangle formed by (5, 6), (8, 9) and (2, 1).

Q25.   Show that the points (0, -1), (-2, 3), (6, 7) and (8, 3) are the vertices

           of a rectangle.

Q26.   The points A (0, 3), B (-2, a) and C (-1, 4) are the vertices of a right

           angled triangle at A, find the value of a.

Q27.   Find the value of k for which the points with coordinates (7, 5),

           (k, 11/2) and (2, 6) are collinear.