Coordinate Geometry Problem (1 Viewer)

[frenzal_dude]

ABCD is a parallelogram. The coordinates of A,B and C are (-1,4), (4,6) and (2,7) respectively. Find the coordinates of D.

I got D(1,3) but the answer says: D(-3,5)

Working out:
mAD = (7-6)/(2-4) = -1/2

AD: y = (-1/2)x + 7/2

mBD = (7-4)/(2+1) = 1

BD: y = x + 2

Find the intersection which is the coordinates of D:
(-1/2)x + 7/4 = x + 2

x = 1, y = 3

Please let me know if you get my answer aswell, I'm not sure if the answer given is wrong.

 

[ohexploitable]

D(-3,5) is the correct answer.

 

[frenzal_dude]

How did you get your answer? I tried to find the equation of the two lines which run through D(x,y) and used simultaenous equations to find D, I can't see where I went wrong in my working out.

 

[ohexploitable]

mAD = (7-6)/(2-4) = -1/2

AD: y = (-1/2)x + 7/2

mBD = (7-4)/(2+1) = 1

BD: y = x + 2

lols, how can you find AD and BD if you don't know D?

 

[frenzal_dude]

mAD will be the same as mCB since they are parallel lines.
So then we can easily find AD since we have point A and the gradient.

Likewise for mBD, the gradient will be the same as mAC since they are parallel lines and we have point A, so with that point and knowing the gradient we know the line.

 

[ohexploitable]

lols, silly me :S

 

[frenzal_dude]

ohexploitable you said that (-3,5) is the right answer, can you pls show your working? Can you also show me why my working out is wrong?

 

[frenzal_dude]

I got the right answer now.
Thanks nigga20101, I put D(x,y) in the wrong place when drawing my parallelogram, ofcourse the letters have to go in order.

My first answer is also correct if you don't worry about the order of the letters around the parallelogram.

 

[Drongoski]

Easier this way

The intersection of diagonals AC and BD is M, say. Let co-ords of D be (a,b).

Then M is the common mid-point of segments AC & BD






.: a = -3, b=5

 

[ohexploitable]

ohexploitable you said that (-3,5) is the right answer, can you pls show your working? Can you also show me why my working out is wrong?

I couldn't reply earlier because the internet on my phone decided to be shit and I couldn't get any reception.

 

[Omnipotence]

I couldn't reply earlier because the internet on my phone decided to be shit and I couldn't get any reception.

hahahahaha

 

[ibbi00]

I couldn't reply earlier because the internet on my phone decided to be shit and I couldn't get any reception.

Haha don't be mean to the kid.

 

[ohexploitable]

hahahahaha

Haha don't be mean to the kid.

I being was serious, representing the points as vectors is probably the quickest method.

 

[Omnipotence]

I being was serious, representing the points as vectors is probably the quickest method.

I admired your approach. lol =]

 

[ibbi00]

I being was serious, representing the points as vectors is probably the quickest method.

However, as soon as you try this in the 2U course you will quickly come to realise that it will not yield you any marks as it is not part of the said syllabus.

 

[frenzal_dude]

thats pretty mean u jerk lol , look at the time the account was made and it says "UTS student", I am guessing this person did their hsc in 2007, so that makes them about what , like 21 or 22 atleast. This "kid" is older than you son . I understand you did shit at maths but lets use some logical thinking for once . Perfect example of someone that wrote learn, maths is not about memorising formulas its about logic and deduction and picking up on shit like that.

But then you kinda wonder why someone so old would be asking a question

I'll be 24 in June, did my HSC in 2005.
I got the question right if you consider D to be close to the origin, but strictly speaking the letters should be in alphabetical order around the paralellogram.

And d/w about the complex plane stuff, I did all that in my engineering degree.

 

[ibbi00]

Why are you even doing this question -.-

 

[frenzal_dude]

I know it's an easy question, the only reason i posted it here was coz i was confused why the book had a different answer, both answers are correct depending on where you consider D(x,y) to be.
btw I'm a maths tutor so that's why I put this question up.

 

[ibbi00]

ATARs do not correspond to smarts at all

You're the retard that was putting others down for getting a lower ATAR than yours hence

Going by your logic

 

[NewiJapper]

Just solve it graphically. Draw up points ABC and then go down and left of C like B is to A(but the opposite way lol). That's how I deal with paralellograms lol Save that nasty working out crap for something else more complicated.