One endpoint of a line segment has coordinates represented by (x+4,1/2y). The midpoint of the line segment is (3,−2). How are the coordinates of the other endpoint expressed in terms of x and y?

Step-by-step explanation:

We are given that one of the endpoints of the line segment is:

And that the midpoint of the line segment is (3, -2).

And we want to find the other coordinates in terms of x and y.  

We can consider using the midpoint formula:

We are given that the midpoint is (3,-2). Substitute:

We can solve for each coordinate independently.

x-coordinate:

We have:

One of the two endpoints is (x + 4, 1/2y). Hence, we can substitute x + 4 for x₁:

Solve for the second x-coordinate x₂:

Hence, the x-coordinate of the second point is -x + 2.

y-coordinate:

We have:

We can substitute 1/2y for y₁. This yields:

Solve for y₂:

In conclusion, the other coordinate expressed in terms of x and y is: