Question

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 1

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).