Okay, so I need to find the midpoint of the line segment between the points (-5, 5) and (3, 7). Hmm, let me think. I remember there's a formula for the midpoint between two points. Let me recall... Oh right, the midpoint formula! It's something like taking the average of the x-coordinates and the average of the y-coordinates. So, if the points are (x1, y1) and (x2, y2), the midpoint would be ((x1 + x2)/2, (y1 + y2)/2). Let me check if that makes sense.

Let me visualize the points on a coordinate plane. The first point is (-5,5), which is in the second quadrant, and the second point is (3,7), which is in the first quadrant. The midpoint should be somewhere in between. If I average the x's, -5 and 3. Hmm, (-5 + 3)/2. That's (-2)/2, which is -1. For the y's, 5 and 7. (5 + 7)/2 is 12/2, which is 6. So the midpoint should be (-1, 6). Wait, let me verify that again.

Wait, maybe I should write it out step by step. Let's take the x-coordinates first. The two x's are -5 and 3. Adding them together: -5 + 3 equals -2. Then divide by 2: -2 divided by 2 is -1. That's the x-coordinate of the midpoint. Then the y-coordinates: 5 and 7. Adding them: 5 + 7 is 12. Divided by 2 is 6. So yes, the midpoint is (-1, 6). That seems right.

But just to make sure I didn't make a mistake in arithmetic. Let me check the x part again. -5 + 3. Starting at -5, adding 3 would bring you to -2, right? Because moving 3 units to the right from -5. Then divide by 2. So -2 divided by 2 is indeed -1. For the y part, 5 + 7. 5 plus 7 is 12, divided by 2 is 6. Yep, that checks out.

Alternatively, maybe I can plot these points and see if the midpoint makes sense. Let's see, from (-5,5) to (3,7). The line goes from the left side of the coordinate plane to the right. The midpoint should be exactly halfway between them. If I go halfway in the x-direction from -5 to 3, that's moving 4 units to the right (since 3 - (-5) is 8 units total, so halfway is 4 units from each end). Starting at -5, adding 4 gives -1. Similarly, in the y-direction, from 5 to 7, that's 2 units total, so halfway is 1 unit. So starting at 5, adding 1 gives 6. So that's the midpoint (-1,6). That seems to make sense.

Another way to think about it: if I move from (-5,5) towards (3,7), how much do I move? The change in x is 3 - (-5) = 8. The change in y is 7 - 5 = 2. So the midpoint is halfway, so half of 8 is 4 in x, and half of 2 is 1 in y. So starting at (-5,5), adding (4,1) gives (-1,6). Yep, that's the same result. So that confirms it again.

I think that's solid. The midpoint formula works here, and all the checks confirm that (-1,6) is the correct answer. I don't see any mistakes in my calculations or reasoning. So I'm confident that's the right midpoint.
Therefore, the midpoint of the line segment between $(-5,5)$ and $(3,7)$ is $\boxed{(-1,6)}$.
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