RD Chapter 14 Co ordinate Geometry Ex 14.3 Solutions
Question - 11 : - (i) In what ratio is the line segment joining the points (-2, -3) and (3, 7) divided by the y-axis ? Also find the co-ordinates of the point of division. [CBSE 2006C]
(ii) In what ratio is the line segment joining (-3, -1) and (-8, -9) divided at the point (-5, −21/5) ?
Answer - 11 : -
(i) The point lies on y-axis
Its abscissa is O
Let the point (0, y) intersects the line joining the points (-2, -3) and (3, 7) in the ratio m : n
Question - 12 : - If the mid-point of the line joining (3, 4) and (k, 7) is (x, y) and 2x + 2y + 1 = 0, find the value of k.
Answer - 12 : - Mid-point of the line joining the points (3, 4) and (k, 7) is (x, y)
Question - 13 : - Find the ratio in which the points P (3/4 , 5/12) divides the line segments joining the points A (1/2 , 3/2) and B (2, -5). [CBSE 2015]
Answer - 13 : -
Question - 14 : - Find the ratio in which the line segment joining (-2, -3) and (5, 6) is divided by (i) x-axis (ii) y-axis. Also, find the co-ordinates of the point of division in each case.
Answer - 14 : -
(i) Ordinate of a point on x-axis is zero
Let the co-ordinate of the point on x-axis be (0, x)
But (x, 0) is a point which divides the line segment joining the points (-2, -3) and (5, 6) in the ratio m : n
Question - 15 : - Prove that the points (4, 5), (7, 6), (6, 3), (3, 2) are the vertices of a parallelogram. Is it a rectangle ?
Answer - 15 : -
The vertices of a parallelogram ABCD are A (4, 5), B (7, 6), C (6, 3), and D (3, 2)
The diagonals AC and BD bisect each other at O
O is the mid-point of AC as well as of BD
Question - 16 : - Prove that (4, 3), (6, 4), (5, 6) and (3, 5) are the angular points of a square.
Answer - 16 : -
Let A (4, 3), B (6, 4), C (5, 6) and D (3, 5) are the vertices of a square ABCD.
AC and BD are its diagonals which bisects each other at O.
O is the mid-point of AC
The diagonals of the quadrilateral ABCD are equal and bisect eachother at O and sides are equal
ABCD is a square
Question - 17 : - Prove that the points (-4, -1), (-2, -4), (4, 0) and (2, 3) are the vertices of a rectangle.
Answer - 17 : -
Let the vertices of a quadrilateral ABCD are A (-4, -1), B (-2, -4), C (4, 0) and D (2, 3)
Join AC and BD which intersect eachother at O
If O is the mid-point of AC then its co
Question - 18 : - Find the lengths of the medians of a triangle whose vertices are A (-1, 3), B (1, -1) and C (5, 1).
Answer - 18 : -
The co-ordinates of the vertices of ∆ABC are A (-1, 3), B (1, -1) and C (5, 1)
D, E and F are the mid-points of sides BC, CA and AB respectively
Question - 19 : - Find the ratio in which the line segment joining the pionts A (3, -3) and B (-2, 7) is divided by x-axis. Also, find the coordinates of the point of division. [CBSE 2014]
Answer - 19 : -
Let a point P (x, 0)
x-axis divides the line segment joining the points A (3, -3) and B (-2, 7) in the ratio m1 : m2
Question - 20 : - Find the ratio in which the point P (x, 2) divides the line segment joining the points A (12, 5) and B (4, -3). Also, find the value of x. [CBSE 2014]
Answer - 20 : - Let P (x, 2) divides the line segment joining the points A (12, 5) and B (4, -3) in the ratio m1 : m2