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RD Chapter 14 Co ordinate Geometry Ex 14.2 Solutions

Question - 1 : -
Find the distance between the following pair of points :
(i) (-6, 7) and (-1, -5)
(ii) (a + b, b + c) and (a – b, c – b)
(iii) (a sin α, -b cos α) and (-a cos α, -b sin α)
(iv) (a, 0) and (0, b)

Answer - 1 : -


Question - 2 : - Find the value of a when the distance between the points (3, a) and (4, 1) is √10

Answer - 2 : -


Question - 3 : - If the points (2, 1) and (1, -2) are equidistant from the point (x, y), show that x + 3y = 0.

Answer - 3 : -


Question - 4 : - Find the values of x, y if the distances of the point (x, y) from (-3, 0) as well as from (3, 0) are 4.

Answer - 4 : - Distance between (x, y) and (-3, 0) is

Question - 5 : - The length of a line segment is of 10 units and the coordinates of one end-point are (2, -3). If the abscissa of the other end is 10, find the ordinate of the other end.

Answer - 5 : - Let the ordinate of other end by y, then The distance between (2, -3) and (10, y) is

Question - 6 : - Show that the points (-4, -1), (-2, -4), (4, 0) and (2, 3) are the vertices points of a rectangle. (C.B.S.E. 2006C)

Answer - 6 : -


AB = CD and AD = BC
and diagonal AC = BD
ABCD is a rectangle

Question - 7 : - Show that the points A (1, -2), B (3, 6), C (5, 10) and D (3, 2) are the vertices of a parallelogram.

Answer - 7 : -


Question - 8 : - Prove that the points A (1, 7), B (4, 2), C (-1, -1) and D (-4, 4) are the vertices of a square. [NCERT]

Answer - 8 : -

Vertices A (1, 7), B (4, 2), C (-1,-1), D (-4, 4)
If these are the vertices of a square, then its diagonals and sides are equal

Question - 9 : - Prove that the points (3, 0), (6, 4) and (-1, 3) are the vertices of a right-angled isosceles triangle. (C.B.S.E. 2006C)

Answer - 9 : -


Question - 10 : - Prove that (2, -2), (-2, 1) and (5, 2) are the vertices of a right angled triangle. Find the area of the triangle and the length of the hypotenuse.

Answer - 10 : -


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