Question

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

Answer 1

I would use my trusty Distance Formula, although I'm not sure which is which to plug in.

Answer 2

\[d = \sqrt(x _{2} - x _{1})^2 + (y _{2} - y _{1})^2\]

Answer 3

\[d = \sqrt (a - (-b)^{2} + (0 - c)^2\]

Answer 4

What is it that you are trying to do? Perimeter? Area? Other?

Answer 5

"Find the lengths of the diagonals of this trapezoid."

Answer 6

Okay, first, we should observe symmetry and decide that the two diagonals are the same length. Agreed?

Answer 7

Yes.

Answer 8

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?

Answer 9

Eh, no, that's precisely what I had in mind! :)

Answer 10

Thank you.

Answer 11

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?

Answer 12

My drawing is not entirely accurate, but I only see a scalene triangle and equilateral triangle?

Answer 13

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.

Answer 14

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. :-)