A scientist is plotting the circular path of a particle on a coordinate plane for a lab experiment. The scientist knows the path is a perfect circle and that the particle starts at ordered pair (-5, -11). When the particle is halfway around the circle, the particle is at ordered pair (11,19). The segment formed by connecting these two points has the center of the circle at it’s midpoint. A.)What is the ordered pair that represents the center of the circle? B.) What is the length of the radius, in units, of the circle? C.) Explain why the particle can never pass through a point with an X-coordinate of 24 as long as it stays on the circular path.

Answer 1

As the question suggests, the line joining your two points is a diameter.
So the centre is the midpoint, which is
((-5+11)/2 , (-11+19)/2 )
= (3, 4)

radius = √(3+5)^2 + (4+11)^2
= √(64+225) = √289 = 17

equation of circle:
(x-3)^2 + (y-4)^2 = 289

if x = 24
21^2 + (y-4)^2 = 289
(y-4)^2 = -152
to solve this , we would take √ of both sides, but you can't take the √ of a negative.
So there is point which has x = 24 as its x coordinate.