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RD Chapter 14 Co ordinate Geometry Ex 14.2 Solutions

Question - 31 : - Find the value of x such that PQ = QR where the co-ordinates of P, Q and R are (6, -1) (1, 3) and (x, 8) respectively. [CBSE 2005]

Answer - 31 : -


Question - 32 : - Prove that the points (0, 0), (5, 5) and (-5, 5) are the vertices of a right isosceles triangle. [CBSE 2005]

Answer - 32 : - Let the vertices of a triangle be A (0, 0), B (5, 5) and C (-5, 5)

Question - 33 : - If the points P (x, y) is equidistant from the points A (5, 1) and B (1,5), prove that x = y. [CBSE 2005]

Answer - 33 : -


Question - 34 : - If Q (0, 1) is equidistant from P (5, -3) and R (x, 6) find the values of x. Also find the distances QR and PR. [NCERT]

Answer - 34 : -

Q (0, 1) is equidistant from P (5, -3) and R (x, 6)
PQ = RQ

Question - 35 : - Find the values ofy for which the distance between the points P (2, -3) and Q (10, y) is 10 units. [NCERT]

Answer - 35 : - Distance between P (2, -3) and Q (10, y) = 10

Question - 36 : - If the point P (k – 1, 2) is equidistant from the points A (3, k) and B (k, 5), find the values of k. [CBSE 2014]

Answer - 36 : -

Point P (k – 1, 2) is equidistant from A (3, k) and B (k, 5)
PA= PB

Question - 37 : - If the point A (0, 2) is equidistant from the point B (3, p) and C (p, 5), find p. Also, find the length of AB. [CBSE 2014]

Answer - 37 : -

Point A (0, 2) is equidistant from B (3, p) and C (p, 5)
AB = AC

Question - 38 : -
Name the quadrilateral formed, if any, by the following points, and give reasons for your answers :
(i) A (-1, -2), B (1, 0), C (-1, 2), D (-3, 0)
(ii) A (-3, 5), B (3, 1), C (0, 3), D (-1, -4)
(iii) A (4, 5), B (7, 6), C (4, 3), D (1, 2)

Answer - 38 : -


Question - 39 : - Find the equation of the perpendicular bisector of the line segment joining points (7, 1) and (3, 5).

Answer - 39 : - Let the given points are A (7, 1) and B (3, 5) and mid point be M

Question - 40 : - Prove that the points (3, 0), (4, 5), (-1, 4) and (-2, -1) taken in order, form a rhombus. Also find its area.

Answer - 40 : -


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