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Question
Find the coordinates of point A, where AB is a diameter of the circle with centre (–2, 2) and B is the point with coordinates (3, 4).
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Solution
Let the centre of the circle be O.
Since AB is the diameter so, O is the midpoint of AB.
Thus, using the section formula,
`(a+3)/(2) = - 2`
⇒ `a = -4 - 3 = -7`
And
`(b + 4)/(2) = 2`
⇒ `b = 4 - 4 = 0`
So, the coordinate of point A is (-7,0).
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Assertion (A): Mid-point of a line segment divides the line segment in the ratio 1 : 1
Reason (R): The ratio in which the point (−3, k) divides the line segment joining the points (− 5, 4) and (− 2, 3) is 1 : 2.
