<Question>
Find the midpoint of the line segment between $(-5,5)$ and $(3,7)$. Express your answer as an ordered pair, $(x,y)$.
</Question>

<think>
<Plan_1>
Okay, so I need to find the midpoint of the line segment between the points (-5, 5) and (3, 7). Hmm, midpoints... I remember there's a formula for that. Let me try to recall. I think it's the average of the x-coordinates and the average of the y-coordinates. So, if the two points are (x₁, y₁) and (x₂, y₂), the midpoint would be ((x₁ + x₂)/2, (y₁ + y₂)/2). Let me check if that makes sense.

<prompt_1.1> Verify the midpoint formula by checking if it makes sense using the given points. </prompt_1.1>
</Plan_1>

<Execution_1>
<execution_1.1>
If you have two points, the midpoint is right in the middle between them. So, averaging the x's and y's should give the point exactly halfway. Yeah, that seems right.
</execution_1.1>
</Execution_1>

<Plan_2>
Based on execution_1.1:
Alright, let's apply that formula to the given points. The first point is (-5, 5), so x₁ is -5 and y₁ is 5. The second point is (3, 7), so x₂ is 3 and y₂ is 7. Plugging these into the formula, the x-coordinate of the midpoint would be (-5 + 3)/2, and the y-coordinate would be (5 + 7)/2.

Let me compute the x part first.

<prompt_2.1> Calculate the x-coordinate of the midpoint using the formula and the given points. </prompt_2.1>

Now the y part. 5 + 7 is 12.
Half of 12 is 6. So the y-coordinate is 6.
-----

Wait, let me visualize this. If I plot the two points, (-5,5) is in the second quadrant, and (3,7) is in the first quadrant. The midpoint should be somewhere between them. Moving from (-5,5) to (3,7), the x increases by 8 units (from -5 to 3 is +8), so halfway would be 4 units from each.

<prompt_2.2> Visualize the midpoint by considering the distance between the x and y coordinates. </prompt_2.2>

Another way to check: maybe using distance formula? Wait, no, the midpoint formula is different. The distance formula is for the distance between two points, but midpoint is just the average.

<prompt_2.3> Consider alternative methods to confirm the midpoint formula. </prompt_2.3>

Alternatively, parametric equations. The line from (-5,5) to (3,7) can be parameterized as x(t) = -5 + t*(3 - (-5)) = -5 + 8t, y(t) = 5 + t*(7 -5) = 5 + 2t, where t goes from 0 to 1. The midpoint is at t = 0.5.

<prompt_2.4> Use parametric equations to verify the midpoint. </prompt_2.4>
</Plan_2>

<Execution_2>
<execution_2.1>
-5 plus 3 is... hmm, that's like starting at -5 and moving 3 to the right, which would be -2. So, (-5 + 3) is -2. Then divide by 2: -2/2 = -1. So the x-coordinate is -1.
</execution_2.1>

<execution_2.2>
Starting at x = -5, adding 4 gives x = -1. Similarly, the y-coordinate increases by 2 units (from 5 to 7), so halfway would be 1 unit up from 5, which is 6. So that gives (-1, 6).
</execution_2.2>

<execution_2.3>
But maybe using vectors? The midpoint is the average of the position vectors of the two points. So, adding the vectors and dividing by 2. That's essentially the same as the midpoint formula.
</execution_2.3>

<execution_2.4>
Plugging t = 0.5 into x(t): -5 + 8*(0.5) = -5 + 4 = -1. y(t): 5 + 2*(0.5) = 5 +1 =6. So, same result. That's another method confirming the midpoint is (-1,6).
</execution_2.4>
</Execution_2>

<Plan_3>
Based on execution_2.1:
Wait, let me double-check that. If I start at -5 and add 3, that's -5 +3.
Yes, that's -2. Then divide by 2, so -2 divided by 2 is indeed -1.

Now the y-coordinate: 5 +7 is 12.

<prompt_3.1> Calculate the y-coordinate of the midpoint using the formula and verify it. </prompt_3.1>

Is that right? Let me confirm.
-----

So, putting it all together, the midpoint is (-1, 6). Let me just make sure there's no arithmetic mistake.

<prompt_3.2> Verify the calculations for both coordinates and conclude the midpoint. </prompt_3.2>
</Plan_3>

<Execution_3>
<execution_3.1>
Half of 12 is 6.
</execution_3.1>

<execution_3.2>
For the x: -5 +3 = -2; -2/2 = -1. For the y:5+7=12;12/2=6. Yep, looks good. 

I don't think I made any calculation errors here. The steps are straightforward, just applying the formula. Maybe if I had mixed up the coordinates, but no, I used x₁ with x₂ and y₁ with y₂ correctly.
</execution_3.2>
</Execution_3>

<Final_answer>
Therefore, the midpoint of the line segment between $(-5,5)$ and $(3,7)$ is $\boxed{(-1, 6)}$.
</Final_answer>
</think>