Question

The coordinates of one end of the diameter AB of a circle are A (-2, -3) and the coordinates of diameter are (-2, 0). What will be the coordinates of B?

(a) (2, -3)

(b) (-2, 3)

(c) (2, 3)

(d) (-2, -3)

This question was addressed to me during an interview for a job.

Query is from Geometry in chapter Coordinate Geometry of Mathematics – Class 10

Answer 1

Right choice is (b) (-2, 3)

For explanation I would say: 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(-2, -3) and center is (-2, 0) and the ratio is 1:1

Let the coordinates of other side of the radius be (x, y).

∴ -2 = \(\frac {1(-2)+1(x)}{2} = \frac {-2+x}{2}\)

-4 = -2 + x

-4 + 2 = x

x = -2

0 = \(\frac {1(-3)+1(y)}{2} = \frac {-3+y}{2}\)

0 = -3 + y

y = 3

Hence, the point is (-2, 3).