Question

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

Answer 1

Answer:

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Answer 2

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

Step-by-step explanation:

Given: AB is a diameter of the circle whose centre is (2, -3) and B is (1, 4).

Solution:

Let C be the center. Then C is the mid-point of AB.

Let x, y be the coordinates of A.

Then A(x,y) = mid-point of AB = C

 (x+1/2 , y+4/2) = (2, -3)

We get x+1/2 = 2

x + 1 = 4

Therefore x = 3.

y + 4/2 = -3

y + 4 = -6

y = -10

So co-ordinates of A is (3,-10)

AC must be equal to BC as they are both radius.

d(A, C) = √ (x2 − x1)² + (y2 − y1)² = √(2-3)² + (-3+10)² = √1 + 49 = √50

d(B, C) = √ (2-1)² + (-3-4)² = √ 1 + 49 = √50