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Question
The coordinates of diameter AB of a circle are A(2, 7) and B(4, 5), then find the coordinates of the centre
Solution
Let C(x, y) be the centre of the circle,
A(x1, y1) = A(2, 7), B(x2, y2) = B(4, 5)
∴ x1 = 2, y1 = 7, x2 = 4, y2 = 5
C is the mid-point of seg AB.
∴ By midpoint formula,
C(x, y) = `((x_1 + x_2)/2, (y_1 + y_2)/2)`
= `((2 + 4)/2, (7 + 5)/2)`
= `(6/2, 12/2)`
∴ C(x, y) = C(3, 6)
∴ The co-ordinates of the centre of the circle are (3, 6).
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