Question

Find the lengths of the diagonals of this trapezoid.

Answer 1

Do you know the distance formula?

Answer 2

d=(x2-x1)^2 + (y2-y1)^2

Answer 3

Yes. If you take the square root of the right hand side expression that is it.

Answer 4

Using the points (-b,c) and (a,0) will give you the length of one diagonal.

Answer 5

Using the points (b,c) and (-a,0) will give you the length of the other diagonal.

Answer 6

Is that all I have to do?

Answer 7

yes. I would simplify each expression enough to show that the diagonals are congruent.

Answer 8

How would I do that exactly?

Answer 9

Plug in the first point and post the result.

Answer 10

to the distance formula?

Answer 11

Yes. Plug the points (-b,c) and (a,0) into the distance formula.

Answer 12

I got (a + b , c) for the first equation and the same for the second time (a + b , c).
Is that correct?

Answer 13

Here is the distance formula:
\[d=\sqrt{(x _{2}-x _{1})^2-(y _{2}-y _{1})^2}\]

Answer 14

Plug the points into that.

Answer 15

I did that and I got ( a+b,c)

Answer 16

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

Answer 17

Now, how in the world did you get (a+b,c) out of that?

Answer 18

I simplified from where you left off.

Answer 19

\[\sqrt{9+16}= ???\]

Answer 20

What is the answer to that example?

Answer 21

5

Answer 22

By your logic in the previous example, it would be 3+4

Answer 23

Why would it be that instead of 5 if you were to add 9+16=25. square 25 to get 5. What you did was like extending or whatever is the correct term you just did, to get 3+4

Answer 24

So if that answer is 5, (which it is) then how can this:
\[\sqrt{(x _{2}-x _{1})^2+(y _{2}-y _{1})^2}=(x _{2}-x _{1}+(y _{2}-y _{1})\]

Answer 25

What you just did was take apart the (x2-x1)^2 +(y2-y1)^2 because it was squared

Answer 26

You are the one who said that:
\[\sqrt{(a+b)^2+c^2}=(a+b)+c\]

I am just trying to convince you that it is false.

Answer 27

ok. So would (a+b)^2 + c^2 have a 2 in front since its twice of itself?

Answer 28

\[\sqrt{(a+b)^2+c^2}\]

Answer 29

That's what it would be.

Answer 30

That's all?

Answer 31

yes

Answer 32

Then what about the other equation?

Answer 33

Do the same thing but use the points ((b,c) and (-a,0)

Answer 34

Won't it be the same since it's supposed to be congruent to the other diagonal?

Answer 35

It's up to you to show that. The problem said to find the lengths of the diagonals. That's plural.

Answer 36

Thanks for your help

Answer 37

yw