Why does dividing the final(chosen) height in a line by 2 give you the average height(y) in that line?

Question

I was taught, of course, that the average of something is the sum of all the parts divided by the number of those parts.

This is easy when it is a set of values(2, 6, 8) because its simply (2+6+8)/3 = 16/3 ≈ 5.33.

But when you have a line, you have an **infinite amount of values** divided by **infinity**, right?

So how is it even possible to take the average? And why can you simply divide it by 2 when its a line?

And then of course there is the question about the average of curves and whatnot…

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I feel so dumb, plz help me understand.

**Also this question comes from the idea that average velocity is half the final velocity**

In: 0

Answer 1

It’s a line, so it won’t change direction, we know that.

So if we take the sum of two points in the line, and divide by 2, we get the average between two points. We can also take 3 points in the line, add them together, and divide by 3, and we get the average between those points.

The start and end points are just two points on the line.

If I drive 30 miles in 1 hour, my average speed was 30mph. You know this even though I only told you how far I got from the start and how long it took to get there.