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Question:

If the coordinates of the one end of a diameter of a circle are (2,3) and the coordinates of its centre are (-2,5), then the coordinates of the other end of the diameter are:

(6,7)

(-6,7)

(6,-7)

(-6,-7)

Solution:

Let the coordinates of the one end of a diameter AB of a circle are A(2,3) and B(x,y). Let the coordinates of the center of the circle C(-2,5). As center is the midpoint of the diameter AB so the coordinates of center is C((2+x)/2, (3+y)/2). Now equating the coordinates of center we get (2+x)/2 = -2; => 2+x = -4 => x = -4-2; => x = -6; (3+y)/2 = 5 => 3+y = 10 => y = 10-3 => y = 7. Therefore, Coordinates of B = (-6,7).