Question

the centre c of circle has coordinate4,5) and one point on circumference is (8,10). find the coordinate of other end of diamater

Answer 1

Centre = (4,5)
Radius = distance between (4,5) & (8,10)

equation of radius :
y = (y2-y1/x2-x1) ×x + c
y = 5/4 x + 0
4y-5x = 0


Radius =
√16+25
= √41

Answer 2

let co ordinates of other end of the diameter B (x,y)

centre (O) =(4,5)
another end point A(8,10)

O is the mid point of AB

mid point of joining two points (x1,y1) and (x2,y2) = (x1+x2/2, y1+y2/2)


midpoint of joining of (x1,y1)=A(8,10) and (x2,y2)=B(x,y) = O(4,5)

(8+x/2,10+y/2) =(4,5)

therefore
(8+x)=4*2 and (10+y)=5*2 since x co ordinates and y co ordinate are equal
8+x=8 and 10+y =10
x=8-8 and y= 10-10
x= 0 and y=0

required point B(x,y) = (0,0)