College Algebra MATH 107

Question

Points (–5, 6) and (–7, 2) are endpoints of the diameter of a circle

 

(a) What is the length of the diameter? Give the exact answer, simplified as much as possible.
Show work.

(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.

Answer 1

a)

 

Use the distance formula.

 

d = √[(x₁ - x₂)² + (y₁ - y₂)²]

 

where:

(x₁ , y₁) = (-5, 6)

(x₂ , y₂) = (-7, 2)

d is the diameter

 

 

b)

 

Use the midpoint formula.

 

M = ((x₁ + x₂) / 2 , (y₁ + y₂) / 2)

 

where  M is the centerpoint C.

 

Plug in the known values from part a.

 

 

c)

 

The point that is symmetric to C about the x-axis is  C'(x, -y).  You simply keep the x-coordinate and negate the y-coordinate of point C.