Question

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

Answer 1

I think you satisfies with my answer

Answer 2

$\huge{ \underline{ \boxed{ \sf{ \red{Required \: AnsweR}}}}}$

• Given : AB is the diameter of the circle. The coordinates of B are (1,4)

Let us take the midpoint as P, whose coordinates are (2,-3)

• To Find : The coordinates of A.

Let us take the coordinates of A as (x,y)

Using the midpoint formula,

⟹ P = $( \frac{x1 + x2}{2} \: , \frac{y1 + y2}{2})$

Where P is the midpoint.

The coordinates of P are (2,-3) as given in the question.

So,

$(2 , - 3) = ( \frac{x1 + x2}{2} , \frac{y1 + y2}{2} )$

$\frac{x + 1}{2} = \frac{2}{1}$

$\sf{Cross \: Multiplying \: The \: Whole \: Thing,}$

$\sf{ 1(x + 1) = 2(2)}$

$\sf{x + 1 = 4}$

$\boxed{\sf{ \blue{x = 3}}}$

$\frac{y + 4}{2} = \frac{-3}{1}$

$\sf{Cross \: Multiplying,}$

$\sf{ 1(y + 4) = 2( - 3)}$

$\sf{y + 4 = - 6}$

$\sf{ y = - 6 - 4}$

$\boxed{\sf{ \red{y = - 10}}}$

So, the coordinates of A are (3,-10)