Help with question please.

Question

Can someone please help me with this question. I have no idea how to solve this question nor know the formula on which I am supposed to be using to solve this equation. The one thing I do know is part b on finding the center point C of the circle which I listed below.

 

Points (-7,5) and (-3,1) 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.

 

b) What is the center point C of the circle?

 

-3+(-7)/2                       1+5/2

-10/2                                6/2

=-5                                      =3

 

Center of the circle would be (-5,3)

 

c) Given the point C you found in part (b), state the point symmetric to C about the y-axis.

Answer 1

To answer a), use the distance formula with (x₁, y₁) = (-7, 5) and (x₂, y₂) = (-3, 1):

 

d = √[(x₂ - x₁)² + (y₂ - y₁)²] = √[(-3 - (-7))² + (1 - 5)²] = √[4² + (-4)²] = √(16 + 16) = √32 = 4√2 .

 

You found the correct center by finding the midpoint of the given diameter.

 

For c), the point symmetric to the y-axis has the x-coordinate change in sign. So, that point would be (5, 3).