Question

Need helpp with coordinate proofs

Answer 1

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Answer 2

You can use the distance formula (or same-wise, the Pythagorean theorem).

The distance between any two points \((x_1,y_1)\) and \((x_2,y_2)\) is:
\(\color{blue}{{\rm D}=\displaystyle \sqrt{(y_2-y_1)^2+(x_2-x_1)^2}}\)

Answer 3

Okay, is a formula the same thing as expression?

Answer 4

You need the formula to find the expression.

Answer 5

your points (you can use any diagonal, let's use the one going NE).

Answer 6

So, your points are (0,0) and (a,b).
APPLY THE FORMULA to THESE POINTS.

Answer 7

Okay. Does (a,b) need an exact number coordinate or do I just use (a,b) as it is?

Answer 8

use a and b.

Answer 9

Okay. :)

Answer 10

For example the distance between \((\alpha,\beta)\) and \((\alpha +4,~\beta+3)\) is:

\({\rm D}=\displaystyle \sqrt{([\alpha+4]-\alpha)^2+([\beta+3]-\beta)^2}=\sqrt{(4)^2+(3)^2}=\sqrt{25}=5\)

Answer 11

but, in your case, your answer will contain a and b (they won't cancel like they did in my example)

Answer 12

Okay so mine will look like this \[D=\sqrt{(a _{2}-0_{1})^{2}+(b _{2}-0_{1})}\]

Answer 13

I forgot the 2 at the end of it.

Answer 14

Your points are \((\color{darkgoldenrod}{0},\color{red}{0})\) and \((\color{green}{a},\color{blue}{b})\). So you will have:

\(\color{black}{{\rm D}=\displaystyle \sqrt{(\color{blue}{b}-\color{red}{0})^2+(\color{green}{a}-\color{darkgoldenrod}{0})^2}}\)

Answer 15

Oh okay, I see.

Answer 16

(you don't need to add the subscripts, they are not part of the formula, rather just the coordinates were denoted by them ....)

Answer 17

So, this expression for D simplifies to ?

Answer 18

\(\color{black}{{\rm D}=\displaystyle \sqrt{(\color{blue}{b}-\color{red}{0})^2+(\color{green}{a}-\color{darkgoldenrod}{0})^2}}\)

Well, you know
\(b-0=b\) and,
\(a-0=a\).

Right?

Answer 19

Yes

Answer 20

Ok, so them please write the most simplified expression for D.
(nothing tricky, just subtract whatever you can)

Answer 21

\[D=a+b\]

Answer 22

incorrect.

Answer 23

\(\color{black}{{\rm D}=\displaystyle \sqrt{(\color{blue}{b}-\color{red}{0})^2+(\color{green}{a}-\color{darkgoldenrod}{0})^2}=\displaystyle \sqrt{\displaystyle b^2+ \displaystyle a^2}}\)

Answer 24

Did I do something wrong? Can you tell me?

Answer 25

I don't know how you got
D = a + b.

Answer 26

If you want me to identify the mistake you made, can you show me how you got D=a+b?

Answer 27

You told me to subtract it and I got D=a+b?

Answer 28

I told you tom subtract b-0 and a-0, which should give you b and a respectively. And then you end up with what I have. (You still haven;t shown me how you got D=a+b.)

Answer 29

Nevermind, I got it.