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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: