Find the length of the radius of a circle with center at 4,2 and a point on the circle at -8,6. Determine the coordinates of the other endpoint of its diameter.

Question

Division of a line segment

Answer 1

Equation of circle is (x-4)^2+(y-2)^2=r^2. Plug in (-8,6):

144+16=160=r^2, so r=√160=4√10=12.65 approx

The end of the diameter at (-8,6) has x coord is distance 4-(-8)=12 from the centre, and the y coord is 6-2=4 from the centre. the opposite end of the diameter must also be  12 to the right of centre=12+4=16 for the x coord, and 4 below the centre for the y coord: 2-4=-2, so the coord is (16,-2).