Coordinates of a point on a cirle.

[Guest]

A circle is centered at point (3,4). The endpoints of a diameter are A and B.
The coordinates of point A are (-2,1). What are the coordinates of point B?

[Guest]

(-2+a)/2 = 3 <=> a=8
(1+b)/2 = 4 <=> b=7

B=(8,7)

[Guest]

I am sorry but I do not understand the solution.

[leesajohnson]

By solving this equations you will find the correct answer
(-2+a)/2 = 3 <=> a=8

(1+b)/2 = 4 <=> b=7

B=(8,7)

[Guest]

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I assume you want it explained rather than just done over again as per last post......

The diameter has end points A and B, we know A and are trying to find B.

A has the coordinates (-2,1) also the centre of the circle will be the mid point of the diameter at (3,4)

We can resolve separately the X and Y co-ordinates of each point to find the X and Y of B ......

The mid point between any 2 points is the sum of the co-ordinates divided by 2. (example... same as mid between 6 and 12 is 18/2 = 9)

Take "X" direction first.....

So........ [("X" of A) + ("X" of B)]/2 = ("X" of centre)

So........ [(-2) + ("X" of B)]/2 = (3)

Gives...... [(-2) + ("X" of B)] = 2 x (3)

Gives....... ("X" of B) = [2 x (3)] - (-2)

Gives......... ("X" of B) = 6 + 2 = 8 is the X coordinate of B


Then take "Y" direction next.....

So........ [("Y" of A) + ("Y" of B)]/2 = ("Y" of centre)

So........ [(1) + ("Y" of B)]/2 = (4)

Gives...... [(1) + ("Y" of B)] = 2 x (4)

Gives....... ("Y" of B) = [2 x (4)] - (1)

Gives......... ("Y" of B) = 8 - 1 = 7 is the Y coordinate of B


So the co-ordinates of B (X,Y) are (8,7)

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