Question

One of the end-points of a circle having centre at origin is A(3,-2), then the other end-point of the diameter has the coordinates.select a proper option (a), (b), (c) or (d) from given options so that the statement becomes correct.
(a) (–3, 2)
(b) (3/2,1)
(c) (3/2,-1)
(d) None of these

Answer 1

one of the end - points of a circle having centre at origin is A(3, -2), then the other end -point of the diameter has the coordinates.

Let other end -point of the diameter is B(x, y)
we know, centre of circle divides two equal parts of diameter. or we can say that centre is the midpoint of diameter.

use midpoint section formula,
if (x1,y1) and (x2,y2) are two points
then, midpoint = [(x1+x2)/2, (y1+y2)/2]

in question, two points A(3,-2) and B(x,y)
and midpoint is O(0,0)
so, 0 = (3 + x)/2 => x = -3
and 0 = (-2 + y)/2 => y = 2

hence, other end-point of diameter is (-3,2)
therefore, (-3,2) is correct.

Answer 2

Given that end points of the circle having centre at origin(0,0) is A(3,-2).

Let the coordinates of B be (x,y).

$= > (0,0) = (\frac{x + 3}{2}), (\frac{y - 2}{2})$

= > (x + 3 ) = 0 and y - 2 = 0

= > x = -3, y = 2.

Therefore, the coordinates of B are (-3,2) ---- Option (A).

Hope this helps!