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A circle in the standard (x,y) coordinate plans has center C(-1,2) and passes through A(2,6). Line segment AB is a diameter of this circle. What are the coordinates of point B?

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Answer: The coordinates of B is (-4, -2)

We know that center is the midpoint of the diameter.

So C(-1,2) is the midpoint of A(2,6) and B(x, y).

The midpoint of  A(2,6) and B(x, y) is = [tex]\left(\frac{x+2}{2},\frac{y+6}{2}\right)[/tex]

Comparing it with C we get:

[tex]\frac{x+2}{2}=-1\\x=-4\\\\\\\frac{y+6}{2}=2\\y=-2[/tex]

So B = (x, y) = (-4 , -2).

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