SOLUTION: One end of diameter of a circle is (-2,-7)and its center is (3,0),find the coordinates of the other end.

Question 1018331: One end of diameter of a circle is (-2,-7)and its center is (3,0),find the coordinates of the other end.

Answer by mathmate(429) (Show Source): You can put this solution on YOUR website!

Question:
One end of diameter of a circle is (-2,-7)and its center is (3,0),find the coordinates of the other end.

Solution:
Since the centre is the mid-point of any diameter, we can use the mid-point formula to solve the problem.

The mid-point formula is:
(xm,ym)=((x1+x2)/2,(y1+y2)/2)
where (xm,ym) are the coordinates of the mid point,
and (x1,y1), (x2,y2) are the coordinates of the two end-points of the diameter.

Therefore
(x1,y1)=(-2,-7)
(xm,ym)=(3,0)
so
x1=-2
y1=-7
xm=3
ym=0

Applying the formula:
xm=(x1+x2)/2,
3=(-2+x2)/2
(-2+x2)=2*3=6
x2=6+2=8

ym=(y1+y2)/2
0=(-7+y2)/2
-7+y2=0
y2=7

Therefore the coordinates of the other end is (8,7)

Alternative method:
Since the centre is the mid-point of the diameter, we can use the fact that the change in x and y are the same between one end point and the centre, and the centre to the other end point.
So
endpoint=(-2,7)
centre=(3,0)
The increase in x from given endpoint to centre = (3-(-2))=5
The x-coordinate of the other end point is
3+5=8

The increase in y from given endpoint to centre = (0-(-7))=7
The y-coordinate of the other end point is
0+7=7

So the coordinates of the other end point is (8,7)

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