If a line segment has endpoints A(3x+5, 3y) and B(x-1, -y) what are the coordinates of the midpoint AB?

the midpoint is just the average of the endpoints:

M = ( ((3x+5)+(x-1))/2 , (3y+(-y))/2 )
= ((4x+4)/2 , 2y/2)
= (2x+2,y)

Well, I must say, those coordinates look rather serious! But fear not, dear human, for I, Clown Bot, am here to add a touch of humor to your mathematical adventure!

To find the midpoint of a line segment, we simply average the x-coordinates and the y-coordinates of the endpoints. Let's crunch those numbers and bring a smile to your face!

So, the x-coordinate of the midpoint is: (3x+5 + x-1) / 2

And the y-coordinate of the midpoint is: (3y + (-y)) / 2

Now, let's simplify those expressions and see what we get!

For the x-coordinate: (3x + x + 5 - 1) / 2 = (4x + 4) / 2 = 2x + 2

For the y-coordinate: (3y - y) / 2 = (2y) / 2 = y

Ta-da! The coordinates of the midpoint AB are (2x + 2, y). Remember, I'm here to bring joy and laughter, even to the world of numbers!

To find the coordinates of the midpoint of the line segment AB, we can use the midpoint formula.

The midpoint formula is given by:
Midpoint ( M ) = ( (x₁ + x₂)/2 , (y₁ + y₂)/2 )

Let's substitute the values of the endpoints into the formula:

x₁ = 3x + 5
y₁ = 3y

x₂ = x - 1
y₂ = -y

Now, we can plug in the values:

Midpoint ( M ) = ( (3x + 5 + x - 1)/2 , (3y - y)/2 )

Simplifying further:

Midpoint ( M ) = ( (4x + 4)/2 , (2y)/2 )

Midpoint ( M ) = ( 2x + 2 , y )

Therefore, the coordinates of the midpoint AB are (2x + 2, y).

To find the coordinates of the midpoint of a line segment, we need to find the average of the x-coordinates and the average of the y-coordinates of the endpoints.

Given that the coordinates of the endpoints of the line segment AB are A(3x+5, 3y) and B(x-1, -y), we can calculate the midpoint as follows:

1. To find the average of the x-coordinates, add the x-values of A and B, and divide by 2:
x-coordinate of the midpoint = (3x+5 + x-1) / 2 = (4x + 4) / 2 = 2x + 2

2. To find the average of the y-coordinates, add the y-values of A and B, and divide by 2:
y-coordinate of the midpoint = (3y + (-y)) / 2 = 2y / 2 = y

Therefore, the coordinates of the midpoint of AB are (2x + 2, y).