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RD Chapter 14 Co ordinate Geometry Ex 14.2 Solutions

Question - 51 : - An equilateral triangle has two vertices at the points (3, 4), and (-2, 3). Find the co-ordinates of the third vertex.

Answer - 51 : - Let two vertices of an equilateral triangle are A (3,4), and B (-2,3) and let the third vertex be C (x, y)

Question - 52 : - Find the circumcentre of the triangle whose vertices are (-2, -3), (-1, 0), (7, -6).

Answer - 52 : -


Question - 53 : - Find the angle subtended at the origin by the line segment whose end points are (0, 100) and (10, 0).

Answer - 53 : -

Let co-ordinates of the end points of a line segment are A (0, 100), B (10, 0) and origin is O (0, 0)
Abscissa of A is 0
It lies on y-axis
Similarly, ordinates of B is 0
It lies on x-axis
But axes intersect each other at right angle
AB will subtended 90° at the origin
Angle is 90° or π/2

Question - 54 : - Find the centre of the circle passing through (5, -8), (2, -9) and (2, 1).

Answer - 54 : -


Question - 55 : - If two opposite vertices of a square are (5, 4) and (1, -6), find the coordinates of its remaining two vertices.

Answer - 55 : -

Two opposite points of a square are (5, 4) and (1, -6)
Let ABCD be a square and A (5, 4) and C (1, -6) are the opposite points
Let the co-ordinates of B be (x, y). Join AC

Question - 56 : - Find the centre of the circle passing through (6, -6), (3, -7) and (3, 3).

Answer - 56 : - Let O is the centre of the circle is (x, 7) Join OA, OB and OC

Question - 57 : - Two opposite vertices of a square are (-1, 2) and (3, 2). Find the co-ordinates of other two vertices.

Answer - 57 : -


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