The coordinates of the ends of the diameter AB of a circle are A (-4, 7) and B(4, 7). What will be the coordinates of the center of the circle?(a) (0, -8)(b) (0, 8)(c) (0, 7)(d) (0, -7)I have been asked this question in a national level competition.This key question is from Geometry topic in portion Coordinate Geometry of Mathematics – Class 10

The coordinates of the ends of the diameter AB of a circle are A (-4,

1.	The coordinates of the ends of the diameter AB of a circle are A (-4, 7) and B(4, 7). What will be the coordinates of the center of the circle?(a) (0, -8)(b) (0, 8)(c) (0, 7)(d) (0, -7)I have been asked this question in a national level competition.This key question is from Geometry topic in portion Coordinate Geometry of Mathematics – Class 10
Answer» CORRECT ANSWER is (C) (0, 7) Easiest explanation: We know that the diameter is TWICE the radius. Hence, the center is the midpoint of the diameter. Using, section formula x = \(\frac {mx_2+nx_1}{m+n}\) and y = \(\frac {my_2+ny_1}{m+n}\) The points are A(-4, 7) and B(4, 7) and the RATIO is 1:1 ∴ x = \(\frac {1(-4)+1(4)}{2} = \frac {0}{2}\) = 0 y = \(\frac {1(7)+1(7)}{2} = \frac {7+7}{2} = \frac {14}{2}\) = 7 Hence, the point is (0, 7).

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