Points (3,2) and (-5,6) 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?

c) given the point c you found in part (b) state the point symmetric to c about the x-axis.

A.8 B.(-1,4) C.(1,4)

Step-by-step explanation:

First, know that (3,2)=(x1,y1) and (-5,6)=(x2,y2)

A. The diameter is 8, given the diference between x1 and x2: 3-(-5)=8

B. The center point is given by (x1+x2)/2 and (y1+y2)/2

(x1+x2)/2 and (y1+y2)/2 = (3-5)/2 and (2+6)/2 = (-1,4)

C. The symmetric point of C about the x-axis is (1,4)

d, x=8

step-by-step explanation:

simplifying

4x + -5 = 2x + 11

reorder the terms:

-5 + 4x = 2x + 11

reorder the terms:

-5 + 4x = 11 + 2x

solving

-5 + 4x = 11 + 2x

solving for variable 'x'.

move all terms containing x to the left, all other terms to the right.

add '-2x' to each side of the equation.

-5 + 4x + -2x = 11 + 2x + -2x

combine like terms: 4x + -2x = 2x

-5 + 2x = 11 + 2x + -2x

combine like terms: 2x + -2x = 0

-5 + 2x = 11 + 0

-5 + 2x = 11

add '5' to each side of the equation.

-5 + 5 + 2x = 11 + 5

combine like terms: -5 + 5 = 0

0 + 2x = 11 + 5

2x = 11 + 5

combine like terms: 11 + 5 = 16

2x = 16

divide each side by '2'.