Question

Help? Geometry Question.

Answer 1

Question?

Answer 2

@whpalmer4 Do you know how to do this as well?

Answer 3

@tootzrll

Answer 4

sorry idk geometry :/

Answer 5

Its ok lol idek either XD

Answer 6

xDDDD

Answer 7

okay, I can help with this.

if you have a line segment, the midpoint of that line segment is just the average of the x values of the endpoints and the average of the y values of the endpoints

Answer 8

so a line segment from (1,2) to (3,4) has a midpoint at (2,3) because (1+3)/2 = 2 and (2+4)/2 = 3

Answer 9

Oh ok. It also gets a little more difficult though when they include letters like on my problem.

Answer 10

So

Q is (2b,2c)
P is (0,0)
and R is (2a,0)

So what do i do next?

Answer 11

Okay, you need to find the location of X. X is a midpoint on what line segment?

Answer 12

PQ ?

Answer 13

Is that right??

Answer 14

yes, it is the midpoint of PQ. What are the coordinates of the endpoints of PQ?

Answer 15

Q is (2b,2c)
P is (0,0)

Answer 16

okay, what do you get if you add the x-values there together, and divide by 2? and do the same with the y-values.

Answer 17

(1b,1c)?

Answer 18

(b,c)

Answer 19

yep!

Answer 20

So x=(b,c)

Answer 21

Yes

Can you repeat the process and find Y?

Answer 22

I think so. (ba,c)?

Answer 23

what is \(2a+2b=\)

Answer 24

it isn't \(2ab\), is it?

Answer 25

Yes..? lol im sorry my brain isnt working today. I have been working on math for hours

Answer 26

(by the way sorry if im taking a long time to ee ur msgs... My computer isnt loading them so i have to keep refreshing)

Answer 27

the endpoints of the line segment on which Y appears are (2a,0) and (2b,2c), right?

so the x value of the midpoint will be \[\frac{2a+2b}{2} = a+b\]
and the y value of the midpoint will be \[\frac{0+2c}{2} = c\]agreed?

Answer 28

\[Y = (a+b,c)\]

Answer 29

Okay yes.

Answer 30

so, first two down, now we have to find the slope of that line segment XY. Do you know how to do that?

Answer 31

Kinda, im not very good at it though.

Answer 32

slope between two points \((x_1,y_1), (x_2,y_2)\) is

\[m = \frac{y_2-y_1}{x_2-x_1}\]

Answer 33

Ok. got it. It seems hard to do with variables though.

Answer 34

no, but different than you are used to...

let's let X be \((x_1,y_1)\) and Y be \((x_2,y_2)\)

can you write out the equation?

Answer 35

Maybe...

X=(b,c) Y=(a,b,c) ? I think im wrong aha

Answer 36

If X is \((x_1,y_1)\), then \(x_1 =\)

Answer 37

b?

Answer 38

is that an answer, or a prayer? :-)

Answer 39

Not sure XD haha. a guess??

Answer 40

We did work out that X is \((b,c)\)
So if we decide that we will set \((x_1,y_1) = X\), that means \((x_1,y_1) = (b,c)\)
Is there any reason to need to guess when I ask you to tell me what \(x_1=\)?

Answer 41

if \((x_1,y_1) = (b,c)\) then \(x_1 = b\). and similarly, \(y_1 = c\). right?

Answer 42

Yes

Answer 43

okay, good. Now, we also found the coordinates of Y. Can you do that same process to find the values of \((x_2,y_2) = Y\), please?

Answer 44

(c,bc)

Answer 45

Oops wait that isnt right i did both Y's

Answer 46

(a,bc)

Answer 47

Is that correct?

Answer 48

Didn't we say \[Y=(a+b,c)\]
You keep changing additions to multiplications...that's going to get you many wrong answers...

Answer 49

Oh right i forgot the + sign

Answer 50

If \[Y=(a+b,c)\]and \[Y = (x_2,y_2)\]then
\[x_2=\]\[y_2=\]

Answer 51

x2 = a+b
y2= c

Answer 52

Sorry for some reason i kept putting B in the y2 part.

Answer 53

Hello?

Answer 54

sorry, working at my other computer

yes, that is correct. so if we plug all of that into the formula:
\[m = \frac{y_2 - y_1}{x_2-x_1}\]we get
\[m = \frac{(c) - (c)}{(a+b) - (b)}\]Agree, disagree?

Answer 55

That seems correct to me

Answer 56

okay, simplify that and give me the value of \(m\), please — that is the slope of line segment XY

Answer 57

C/ab ?

Answer 58

Is that not right?

Answer 59

ok, you're back to your old tricks of converting addition to multiplication :-(

\[m = \frac{(c) - (c)}{(a+b) - (b)}\]What does \((c) - (c) = \)

Answer 60

0

Answer 61

wait would it be C over A?

Answer 62

Wait no just A..?

Answer 63

(Sorry i have to go soon :( )

Answer 64

yes, the two points have the same value of \(y\)! therefore, the slope is 0.

\[m = \frac{(c) - (c)}{(a+b) - (b)} = \frac{0}{a} = 0\]

Answer 65

hopefully, a moment of reflection will give you the slope of line segment PR as well

Answer 66

Yay! Do u have any time to help me and check over PR really quick?

Answer 67

If not its alright. Thanks so much for all your help though.

Answer 68

P be (x1,y1) and R be (x2,y2)

P= 0,0 and R = 2a,0

y2−y1 = 0-0 and x2-x1 is 2a-0

So would it be 2a?

Answer 69

I feel like i did that wrong.. But just a guess.

Answer 70

@whpalmer4

Answer 71

Your feeling was correct.

\[m = \frac{y_2-y_1}{x_2-x_1} = \frac{0-0}{2a-0} = \frac{0}{2a} = 0\]

Two points with the same y-value always produce a slope of 0.

If you look at the diagram, those lines are parallel, aren't they?

Answer 72

Oh yes. Thanks so much for all of your help :D