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Need a confirm, please. Am I doing this right?

Mathematics
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I would use my trusty Distance Formula, although I'm not sure which is which to plug in.
\[d = \sqrt(x _{2} - x _{1})^2 + (y _{2} - y _{1})^2\]

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Other answers:

\[d = \sqrt (a - (-b)^{2} + (0 - c)^2\]
What is it that you are trying to do? Perimeter? Area? Other?
"Find the lengths of the diagonals of this trapezoid."
Okay, first, we should observe symmetry and decide that the two diagonals are the same length. Agreed?
Yes.
Super. Now, it appears you started working with (a,0) and (-b,c). It also appears that you are having some notaiton problems. That's probably why you are struggling with it. There are parentheses missing. \(d = \sqrt{(a-(-b))^{2} + (0-c)^{2}} = \sqrt{(a+b)^{2}+(-c)^{2}}\) That's what you had, it's just written with all the symbols int eh right places. Can we do nything else with it?
Eh, no, that's precisely what I had in mind! :)
Thank you.
We might be able to do one more thing. Draw a perpendicular line from (b,c) down to the x-axis. You should see a right triangle. Can we say anything about the relationship of a, b, and c because of this right triangle?
|dw:1357966403862:dw| My drawing is not entirely accurate, but I only see a scalene triangle and equilateral triangle?
No, no, that't not perpendicular to the x-axis. It should hit the x-axis at (b,0), not at (0,0). It is a vertical line segment.
|dw:1357966687931:dw|
That's it. The one on the right is the one I was looking for. Anyway, my little right triangle leads to \((a-b)^{2} + c^{2} = (a-b)^{2} + (-c)^{2}\) and we don't manage to learn anything, so let's just let that go. It can be very useful to poke around a little. In this case, we didn't learn much, but it was worth the effort to learn to communicate better. :-)

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