RD Chapter 14 Co ordinate Geometry Ex 14.3 Solutions
Question - 1 : - Find the coordinates of the point which divides the line segment joining (-1, 3) and (4, -7) internally in the ratio 3 : 4.
Answer - 1 : -
The line segment joining the points A (-1,3) and B (4, -7) is divided into the ratio 3 : 4
Let P (x, y) divides AB in the ratio 3 : 4
Question - 2 : - Find the points of trisection of the line segment joining the points :
(i) (5, -6) and (-7, 5)
(ii) (3, -2) and (-3, -4)
(iii) (2, -2) and (-7, 4) [NCERT]
Answer - 2 : -
(i) The line segment whose end points are A (5, -6) and B (-7,5) which is trisected at C and D
C divides it in the ratio 1 : 2
i.e., AC : CB = 1 : 2
Question - 3 : - Find the coordinates of the point where the diagonals of the parallelogram formed by joining the points (-2, -1), (1, 0) (4,3) and (1, 2) meet.
Answer - 3 : - Let the vertices of the parallelogram ABCD be A (-2, -1), B (1, 0), C (4, 3) and D (1, 2) in which AC and BD are its diagonals which bisect each other at O
Question - 4 : - Prove that the points (3, -2), (4, 0), (6, -3) and (5, -5) are the vertices of a parallelogram.
Answer - 4 : -
Let the vertices of the quadrilateral ABCD be A (3, -2), B (4, 0), C (6, -3) and D (5, -5)
Now co-ordinates of the mid-point of AC
Question - 5 : - If P (9a – 2, -b) divides the line segment joining A (3a + 1, -3) and B (8a, 5) in the ratio 3 : 1, find the values of a and b. [NCERT Exemplar]
Answer - 5 : -
Let P (9a – 2, -b) divides AB internally in the ratio 3 : 1.
By section formula,
Question - 6 : - If (a, b) is the mid-point of the line segment joining the points A (10, -6), B (k, 4) and a – 2b = 18, find the value of k and the distance AB. [NCERT Exemplar]
Answer - 6 : - Since, (a, b) is the mid-point of line segment AB.
Question - 7 : - Find the ratio in which the points (2, y) divides the line segment joining the points A (-2, 2) and B (3, 7). Also, find the value of y. (C.B.S.E. 2009)
Answer - 7 : - Let the point P (2, y) divides the line segment joining the points A (-2, 2) and B (3, 7) in the ratio m1 : m2
Question - 8 : - If A (-1, 3), B (1, -1) and C (5, 1) are the vertices of a triangle ABC, find the length of the median through A.
Answer - 8 : -
In ∆ABC, the vertices are A (-1, 3), B (1, -1) and C (5, 1)
D is the mid-point of BC
Co-ordinates of D will be [(1+5)/2 , (−1+1)/2]
Question - 9 : - If the points P, Q (x, 7), R, S (6, y) in this order divide the line segment joining A (2, p) and B (7,10) in 5 equal parts, find x, y and p. [CBSE 2015]
Answer - 9 : -
Points P, Q (x, 7), R, S (6, y) in order divides a line segment joining A (2, p) and B (7, 10) in 5 equal parts
i.e., AP = PQ = QR = RS = SB
Q is the mid point of A and S
Question - 10 : - If a vertex of a triangle be (1, 1) and the middle points of the sides through it be (-2, 3) and (5, 2), find the other vertices.
Answer - 10 : -
Let co-ordinates of one vertex A are (1, 1) and mid-points of AB and AC are D (-2, 3) and E (5, 2)
Let the co-ordinates of B be (x1, y1) and C be (x2, y2)