Question

Find the cordinates of a point A, where AB is the diameter of a circle whose centre is (2,-3) and B is (1,4).

Answer 1

Let O is the centre of circle
So,The centre of circle divide the diameter into equal radius
For that we need to use mid point formula
O(x=2,y= -3)
A(x1=a,y1=b)
B(x2=1,y2=4)
Mid point formula
x=x1+x2/2
putting the values
2=a+1/2
4=a+1
a=4-1=3
y=y1+y2/2
putting the values
-3=b+4/2
-6=b+4
b= -6-4= -10
So,coordinates of A(3,-10)
I HOPE THIS WILL HELP YOU MARK ME BRAINLIEST

Answer 2

Let AB internally in the ratio 1 : 2

By using section formula.

$\frac{1(1) + 2(2)}{1 + 2} \: \: \: \frac{1(4) + 2( - 3)}{1 + 2} \\ \\ \frac{ 5}{3} + \frac{ - 10}{3}$
= 3, -10....... Ans.