RD Chapter 14 Co ordinate Geometry Ex 14.3 Solutions
Question - 21 : - Find the ratio in which the point P (-1, y) lying on the line segment joining A (-3, 10) and B (6, -8) divides it. Also find the value of y.
Answer - 21 : -
Question - 22 : - Find the coordinates of a point A, where AB is a diameter of the circle whose centre is (2, -3) and B is (1, 4).
Answer - 22 : - AB is the diameter of the circle and O is the centre of the circle
Question - 23 : - If the points (-2, -1), (1, 0), (x, 3) and (1, y) form a parallelogram, find the values of x and y.
Answer - 23 : -
In ||gm ABCD, co-ordinates of A (-2, -1), B (1, 0),C(x, 3) and D(1, y)
AC and BD are its diagonals which bisect eachother at O
Question - 24 : - The points A (2, 0), B (9, 1), C (11, 6) and D (4, 4) are the vertices of a quadrilateral ABCD. Determine whether ABCD is a rhombus or not.
Answer - 24 : -
The co-ordinates of vertices of a quadrilateral ABCD are A (2,0), B (9,1), C (11,6) and D (4, 4)
AC and BD are its diagonals which intersect eachother at O
The co-ordinates of O in both cases are not same.
It is not a parallelogram and also not a rhombus.
Question - 25 : - In what ratio does the point (-4, 6) divide the line segment joining the points A (-6, 10) and B (3, -8) ?
Answer - 25 : - Let the point P (-4, 6) divides the line segment joining the points A (-6, 10) and B (3, -8) in the ratio m1 : m2
Question - 26 : - Find the ratio in which the y-axis divides the line segment joining the points (5, -6) and (-1, -4). Also, find the coordinates of the point of division.
Answer - 26 : -
The points lies on y-axis
Let its coordinates be (0, y)
and let it divides the line segment joining the points (5, -6) and (-1, -4) in the ratio m1 : m2
Question - 27 : - Show that A (-3, 2), B (-5, -5), C (2, -3) and D (4, 4) are the vertices of a rhombus.
Answer - 27 : -
Vertices of a quadrilateral ABCD are A (-3, 2), B (-5, -5), C (2, -3) and D (4, 4)
Join the diagonals AC and BD which intersect each other at O
Question - 28 : - Find the lengths of the medians of a ∆ABC having vertices A (0, -1), B (2, 1) and C (0, 3).
Answer - 28 : -
A (0, -1), B (2, 1) and C (0, 3) are the vertices of ∆ABC
Let D, E and F are the mid points of BC, CA and AB respectively
Question - 29 : - Find the lengths of the medians of a ∆ABC, having the vertices at A (5, 1), B (1, 5) and C (3,-1).
Answer - 29 : - A (5, 1), B (1, 5) and C (3, -1) are the vertices of ∆ABC
Question - 30 : - Find the co-ordinates of the points which divide the line segment joining the points (-4, 0) and (0, 6) in four equal parts.
Answer - 30 : - AB is a line segment whose ends points are A (-4, 0) and B (0, 6)