Find the Coordinates of a Point A, Where AB is a Diameter of a Circle Whose Centre is (2,-3) and B is (1,4) | Bzziii

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







Let the circle be as shown with centre C (2, -3)
Let AB be the diameter of the circle

Since AB is the diameter ,
Centre C must be the mid - point of AB 
Let (x,y)

Since C  is the mid- point of AB

x-coordinate of C = `\frac{x_{1}+x_{2}}{2}`
y-coordinate of C = `\frac{y_{1}+y_{2}}{2}`

Where,



`x_1` = `x` `y_1` = `y` 

`x_2` = 1  `y_1` = 4
`x` Coordinate of C = `\frac{x + 1}{2}`

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

2 `\times` 2 = `x` + 1

4 = `x` + 1

4 - 1= `x`

3= `x`
`y` Coordinate of C = `\frac{y + 4}{2}`

-3 = `\frac{y + 4}{2}`

-3 `\times` 2 = `y` + 1

-6 - 4 = `y`

- 10= `x`

Hence, the coodinates of A (x,y)

= A (3, -10)

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