Points of a circle

Question

I have no idea how to do the questions below. I need help please.

 

Points (-7,6) and (3,8) 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)

 

 

We can use the endpoints to find the length of the diameter.  We can do this by using the distance formula.

 

d = √[(x₁ - x₂)² + (y₁ - y₂)²]

 

d = √[(-7 - 3)² + (6 - 8)²]

 

d = √(100 + 4)

 

s = √(96)

 

d = √12 * √8

 

d = √4  * √3 * √4  * √2

 

d = 4√6

 

 

The diameter is 4√6.

 

 

b)

 

To find the centerpoint of the circle, we need to find the midpoint between the endpoints.  This can be found using the formula

 

C = ( (x₁ + x₂) / 2  ,   (y₁ + y₂) / 2 )

 

C = ( (-7 + 3) / 2  ,  (6 + 8) / 2 )

 

C = (-4 / 2 , 14 / 2)

 

C = (-2 , 7)

 

 

The centerpoint is (-2, 7).

 

 

c)

 

If the centerpoint is (-2, 7), the other point will be (-2, 0) because we want a point symmetrical to C about the x-axis.  To be symmetrical, this point must be a mirror reflection of C.

 

 

The point that is symmetric to C about the x-axis is (-2, -7).