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RD Chapter 14 Co ordinate Geometry Ex 14.2 Solutions

Question - 41 : - In the seating arrangement of desks in a classroom three students Rohini, Sandhya and Bina are seated at A (3, 1), B (6, 4) and C (8, 6). Do you think they are seated in a line ?

Answer - 41 : - A (3, 1), B (6, 4) and C (8, 6)

Question - 42 : - Find a point ony-axis which is equidistant from the points (5, -2) and (-3, 2).

Answer - 42 : -

The point lies on y-axis
Its x = 0
Let the required point be (0, y) and let A (5, -2) and B (-3, 2)

Question - 43 : - Find a relation between x and y such that the point (x, y) is equidistant from the points (3, 6) and (-3, 4). [NCERT]

Answer - 43 : -


Question - 44 : - If a point A (0, 2) is equidistant from the points B (3, p) and C (p, 5), then find the value of p. [CBSE 2012]

Answer - 44 : -

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

Question - 45 : - Prove that the points (7, 10), (-2, 5) and (3, -4) are the vertices of an isosceles right triangle. [CBSE 2013]

Answer - 45 : - Let points are A (7, 10), B (-2, 5) and C (3, -4)

Question - 46 : - If the point P (x, 3) is equidistant from the points A (7, -1) and B (6, 8), find the value of x and And the distance AP. [CBSE 2014]

Answer - 46 : -

Point P (x, 3) is equidistant from the points A (7, -1) and B (6, 8)
PA = PB

Question - 47 : - If A (3, y) is equidistant from points P (8, -3) and Q (7, 6), find the value of y and find the distance AQ. [CBSE 2014]

Answer - 47 : -

Point A (3, y) is equidistant from P (8, -3) and Q (7, 6)
i.e., AP = AQ

Question - 48 : - If (0, -3) and (0, 3) are the two vertices of an equilateral triangle, find the coordinates of its third vertex. [CBSE 2014]

Answer - 48 : -

Let A (0, -3) and B (0, 3) are vertices of an equilateral triangle
Let the coordinates of the third vertex be C (x, y)

Question - 49 : - If the point P (2, 2) is equidistant from the points A (-2, k) and B (-2k, -3), find k. Also, find the length of AP.

Answer - 49 : -

Point P (2, 2) is equidistant from the points A (-2, k) and B (-2k, -3)
AP = BP
Now,

Question - 50 : - Show that ∆ABC, where A (-2, 0), B (2, 0), C (0, 2) and ∆PQR, where P (-4, 0), Q (4, 0), R (0, 4) are similar.

Answer - 50 : -


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