Question

Find the coordinates of a point A, where AB is the diameter of a circle whose center is (2, -3)

And B is (1, 4).​

Answer 1

Explanation of the diagram [ refer attached picture for rough diagram ] :-

➝ AB is diameter of circle with center O.

➝ Co-ordinates of O : (2,-3)

➝ Co-ordinates of B : (1,4)

➝ O is midpoint of line joining points A and B.

Let co-ordinates of A be (a,b).

Now, according to the question :-

$\longrightarrow \rm(2, - 3) = \bigg( \dfrac{a + 1}{2} , \dfrac{b +4}{2}\bigg) \\ \\ \implies \rm2 = \dfrac{a + 1}{2} \\ \\ \implies \rm4 = {a + 1}\\ \\ \implies \rm4 - 1= {a}\\ \\ \implies \rm3= {a} \\ \\ \\ \rm \implies - 3 = \dfrac{b +4}{2} \\ \\ \rm \implies - 6 = {b +4} \\ \\ \rm \implies - 6 - 4 = {b}\\ \\ \rm \implies - 10 = {b}$

Answer :

Co-ordinates of A = (3,-10)

Answer 2

Step-by-step explanation:

$given \: \: coordinates \: of \: \: o \: (2 \: - 3) \\ coordinates \: of \: b \: ( 1 \: \: \: \: 4) \:( x2 \: y2)\\ \\ let \: the \: coordinates \: of a \: be \: x \: and \: y \:( x1 \: y1)respectively \\ \\ by \: mid \: point \: formula \\ \ \\ \frac{x1 + x2} 2 {2} \: \: \: || \: \: \frac{y1 + y2} 2 { - 3} \\ \\ \\ \\ \frac{x + 1}{2} = 2 \: \: \: \: \: \: \: \: \: \: \: || \: \: \frac{ y + 4 }{2} = - 3 \\ \\ x + 1 = 2 \times 2 \: \: \: \: \: \: \: y + 4 = - 3 \times 2 \\ \\ x + 1 = 4 \: \: \: \: y + 4 = - 6 \\ \: \: \\ \\ x = 4 - 1 \: \: \: \: y = - 6 - 4 \\ x = 3 \: \: y = - 10 \\ therefore \: coordinates \: of \: a \: are \: \: (3 \: . \: - 10) \:$