Question - 42 : - The points (3, -4) and (-6, 2) are the extremities of a diagonal of a parallelogram. If the third vertex is (-1, -3). Find the co-ordinates of the fourth vertex.

Answer - 42 : -

Let the extremities of a diagonal AC of a parallelogram ABCD are A (3, -4) and C (-6, 2)

Let AC and BD bisect eachother at O

Question - 43 : - If the co-ordinates of the mid-points of the sides of a triangle are (1, 1), (2, -3) and (3, 4), find the vertices of the triangle.

Answer - 43 : -

Let A (x1, y1), B (x2, y2) and C (x3, y3) be the vertices of the ∆ABC

D, E and F are the mid-points of BC, CA and AB respectively such that their co-ordinates are D (1, 1), E (2, -3) and F (3, 4)

D is mid-point of BC

Question - 44 : - Determine the ratio in which the straight line x – y – 2 = 0 divides the line segment joining (3, -1) and (8, 9).

Answer - 44 : -

Let the straight line x – y – 2 = 0 divides the line segment joining the points (3, -1), (8, 9) in the ratio m : n

Co-ordinates of the point will be

Question - 45 : - Three vertices of a parallelogram are (a + b, a – b), (2 a + b, 2a – b), (a – b, a + b). Find the fourth vertex.

Answer - 45 : -

In parallelogram ABCD co-ordinates are of A (a + b, a – b), B (2a + b, 2a – b), C (a – b, a + b)

Let co-ordinates of D be (x, y)

Join diagonal AC and BD

Which bisect eachother at O

O is the mid-point of AC as well as BD

Question - 46 : - 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.

Answer - 46 : - Two vertices of a parallelogram ABCD are A (3,2), and B (-1, 0) and its diagonals bisect each other at O (2, -5)

Question - 47 : - If the co-ordinates of the mid-points of the sides of a triangle ar6 (3, 4), (4, 6) and (5, 7), find its vertices. [CBSE 2008]

Answer - 47 : - The co-ordinates of the mid-points of the sides BC, CA and AB are D (3, 4), E (4, 6) and F (5, 7) of the ∆ABC

Question - 48 : - The line segment joining the points P (3, 3) and Q (6, -6) is trisected at the points A and B such that A is nearer to P. If A also lies on the line given by 2x + y + k = 0, find the value of k. [CBSE 2009]

Answer - 48 : -

Two points A and B trisect the line segment joining the points P (3, 3) and Q (6, -6) and A is nearer to P

and A lies also on the line 2x + y + k = 0

=> k = -8

Hence k = -8

Question - 49 : - If three consecutive vertices of a parallelogram are (1, -2), (3, 6) and (5, 10), find its fourth vertex.

Answer - 49 : -

A (1, -2), B (3, 6) and C (5, 10) are the three consecutive vertices of the parallelogram ABCD

Let (x, y) be its fourth vertex

AC and BD are its diagonals which bisect each other at O

Question - 50 : - If the points A (a, -11), B (5, b), C (2, 15) and D (1, 1) are the vertices of a parallelogram ABCD, find the values of a and b.

Answer - 50 : -

A (a, -11), B (5, b), C (2, 15) and D (1, 1) are the vertices of a parallelogram ABCD

Diagonals AC and BD bisect eachother at O

Free - Previous Years Question Papers

RD Chapter 14 Co ordinate Geometry Ex 14.3 Solutions

Subscribe Now!