What is the length of the line segment with endpoints (12, 6) and (12,−9) ?

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Since the line has the same x coordinate, (and it's a positive number) we know the line is vertical, and it's on the right side of the coordinate plane. 

The point (12, 6) is in quadrant 1 (top right), and it's 6 points above the x axis.
The point (12, -9) is in quadrant 4 (bottom right), and it's 9 points below the x axis.

6 + 9 = 15

The answer is 15. :)

Hopefully this helps! If you have any more questions or don't understand, feel free to DM me, and I'll get back to you ASAP! :)

Wow. that is a really cool question.