The centre of the circle that can be circumscribed about the triangle is at (-2,-3). Thus, the correct option is D.
What are the coordinates of midpoint of the line segment AB?
Midpoint, as the word suggests, means the point which lies in the middle of something. Midpoint of a line segment means a point which lies in the mid of the given line segment.
Suppose we've two endpoints of a line segment as:
A(p,q), and B(m,n)
Then let the midpoint be M(x,y) on that line segment. Then, its coordinates are:
x = (p+m)/2
and
y = (q+n)/2
For a right-angle triangle, circumscribed in a circle, the radius of the circle is equal to half the length of the hypotenuse. And the centre of the circle lies at half the distance of the hypotenuse. Therefore, the midpoint of hypotenuse is,
x = (-4+0)/2 = -2
y = (-6+0)/2 = -3
Hence, the centre of the circle that can be circumscribed about the triangle is at (-2,-3). Thus, the correct option is D.
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