Points 21 and 85 are endpoints of the diameter of a circle a

Points (2,1) and (8,-5) are endpoints of the diameter of a circle.

a) What is the length of the diameter?
b) What is the center point C of the circle?
c) Given the point C you found in part (b), state the point symmetric to C about the x-axis.

Solution

Points (2,1) and (8,-5) are endpoints of the diameter of a circle.

a) hence the length of the diameter is l=length between the points (2,1) and (8,-5)=sqrt[(8-2)²+(-5-1)²]=sqrt[36+36]=8.48528 [answer]

b) the center point C of the circle is the middle point of the points (2,1) and (8,-5)

so the co-ordinate of the middle point is ([2+8]/2,[1-5]/2)=(5,-2)   [answer]

c)hence point C is (5,-2). so the abssicca is 5 and the ordinate is -2

so from the origin the point is at 5 units to the right and 2 units down.

so the point symmetric to this point C about the x axis is that point which is 5 units to the right but 2 units up

that is by replacing the ordinate by -ordinate

so the point symmetric to C is (5,2) [answer]