Question

one end of the diameter of a circle is (-2,5).
Find the co-ordinates of the other end of it, if the centre of the circle is (2,-1).

Answer 1

by mid point of the two points

[(-2+x)/2 , (5+y)/2] =(2,-1)
(-2+x)/2 =2   ,   (5+y)/2 =-1
-2+x=4   , 5+y =-2
x=6    ,y=-7
the other end is (6,-7)

Answer 2

let one end of the diameter A = (-2,5)
center of the circle O = (2,-1)
we know that center is the midpoint of the diameter is O (2,-1)
so, [ x₁ + x₂/2 , y₁ + y₂/2 ] = (2,-1)
      [ -2 + x₂/2 , 5 + y₂/2 ] = (2,-1)
   we know that co-ordinates are equal
-2 + x₂/2 = 2                                5 + y₂/2 = -1
 -2 +x₂ = 4                                   5 +y₂ = -2
   x₂ = 4 +2                                       y₂ = -2-5
  x₂ = 6                                             y₂ = -7
the co-ordinates of the other end B = (6, -7)