Answer:

Step-by-step explanation:
We know that one of the endpoints of the line segment is (x+4, 1/2y)
The midpoint of the line segment is (3, -2).
And we want to find the other coordinates in terms of x and y.
To do so, we can use the midpoint formula:

Since we know that the midpoint is (3, -2), let's substitute that for M:

Let's solve for each coordinate individually:
X-Coordinate:
We have:

We know that one of the endpoints is (x+4, 1/2y). So, let's let (x+4, 1/2y) be our (x₁, y₁). Substitute x+4 for x₁. This yields:

Solve for our second x-coordinate x₂. Multiply both sides by 2:

Subtract 4 from both sides:

Subtract x from both sides. Therefore, the x-coordinate of our second point is:

Y-Coordinate:
We have:

Substitute 1/2y for y₁. This yields:

Solve for y₂. Multiply both sides by 2:

Subtract 1/2y from both sides. So:

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