Question

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

Answer 1

A circle with centre (2, - 3) and AB is the diameter of circle with B (1,4).

We have to find, Coordinate of point A.

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☯ Let (x,y) be coordinate of point A.

If AB is the diameter of circle, the centre will be the mid - point of AB.

Therefore,

Centre is the mid - point of AB.

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★ Coordinate of centre of circle = (2, -3).

$\sf x - coordinate\; of \;centre = \dfrac{x + 1}{2}$

$\dashrightarrow\sf 2 = \dfrac{x + 1}{2}$

$\dashrightarrow\sf 2 \times 2 = x + 1$

$\dashrightarrow\sf 4 = x + 1$

$\dashrightarrow\sf x = 4 - 1$

$\dashrightarrow{\boxed{\sf{\pink{x = 3}}}}\;\bigstar$

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$\sf y - coordinate\; of\; centre = \dfrac{y + 4}{2}$

$\dashrightarrow\sf - 3 = \dfrac{y + 4}{2}$

$\dashrightarrow\sf - 3 \times 2 = y + 4$

$\dashrightarrow\sf - 6 = y + 4$

$\dashrightarrow\sf y = - 6 - 4$

$\dashrightarrow{\boxed{\sf{\pink{y = - 10}}}}\;\bigstar$

$\therefore\;{\underline{\sf{Hence,\;the\; coordinate\;of\;A\;is\;(3, - 10).}}}$