Linear Equations Help

Can someone please help me with the following questions on linear equations:

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1.
Given the points A (a,3), B (-2,1) and C (3,2), find the possible value of a if the length of AB is twice the length of BC.

2.
Three points have coordinates A(1,7), B(7,5) and C(0,-2) Find:
a) The equation of the perpendicular bisector of AB
b) The point of intersection of this perpendicular bisector and BC.

3.
P and Q are the points of intersection of the line Y/2+X/3=1 with the X and Y axes respectively.
The gradient of QR is 1/2, where R is the point whose x coordinate is 2a, a > 0
a) Find the Y coordinate of R in terms of a
b) Find the value of a if the gradient of PR is -2

4.
Triangle of ABC
Point A = (1,1)
Point B = (-1,4)
Point C = ???

Grandients
AB = -3m
AC = 3m
BC = m

a) Find the value of m
b) Find the coordinates of C
c) Show that AC=2AB

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Thanks a lot guyz, remember to show full workings out.... add me to msn messenger - mtchouston@hotmail.com
Cheers
Thanks

1.

Distance formula : Square root of (x2-x1)^2 + (Y2-Y1)^2

Therefore

AB^2 = (-2-a)^2 +(1-3)^2

= 4+2a-2a+a^2 +4
= a^2 +8

BC^2 = (3--2)^2 + (2-1)^2

= 25 + 1
=26


Therefore

2(a^2+8) = 26

Therefore

a = root 5.



Post Edited (12-23-03 11:24)

ooooooo



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She says brief things, her love’s a pony
My love’s subliminal

Lovely Mika

ahh there's something wrong with that, it doesn't work at all...hehe, sorry.

computers suck for trying to do maths :\

i'm using paper now, gimme a sec and i'll get it right

okies i got it, i made a mistake before.

As i said on MSN, find the equation of AB and BC, then make 2AB = BC

it gets to 2a^2+8a+16 = 26

get 'a' out of that using the quadratic formula, and a = 1 or -5.

Good luck with the others, I can't be bothered

lol what fun they were

Here's mine:

(.) + (.) = .|.






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LMAO!

Woah Mika! Really impressive! :D

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"Treat others with respect and you too will be respected." Oac - ed'c dnia - E ys yldiymmo drec cyt.

When I need Maths help, I know where to come

i just ask my calculator

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ROTF X-Acto... gostas pouco...

"get 'a' out of that using the quadratic formula, and a = 1 or -5."

or just type it into ur gfx calculator :P

i shud be able to do all of those, but its xmas and i can't be assed, and the hwk that was set was to not do any mahs til the new year, unless its calculating how much the round your buying will cost



Sim

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All Hail The New York Giants - Winners of Superbowl XXI, XXV and XLII!

"I'd love to know what goes on in that crazy head of yours sometimes, Sim..." - Locke Cole

you can ask me as well

in the last term at college, I got an average of 97.4% in maths

so, does my name suit well to me ?

PLease Mika or neone else please try and work out the others?!

are you completely incapable of doing ur own homework? :P

I'm doing the #2 atm

I don't mind helping you out, but you should also realise, that getting help like this in the long run, isn't gonna help you at all.

4.
Triangle of ABC
Point A = (1,1)
Point B = (-1,4)
Point C = ???

Grandients
AB = -3m
AC = 3m
BC = m

a) Find the value of m
b) Find the coordinates of C
c) Show that AC=2AB


1) Plot the A and B in to a coordinate system you have drawn on a piece of paper.

2) add a line from A to B, and then you have AB. Unless I have misunderstood the meaning the term "Grandient", you should be able to work out the gradient of AB.

3) Taking the gradient of AB, you can isolate m. You have now answered question a) and have the the gradients for AB, AC and BC.

4) Since you have the gradients for AC and BC, you can draw two lines. The first line stems from A and uses the gradient AC. The other stems from B and uses the gradient from BC. Where AC and BC intersect you have point C. You have now answered question b), and you have a triangle.

5) If the triangle has a right angle, it is a piece of cake, since you have "A squared + B squared = C squared". All you have to do, is to figure out which of AB, AC and BC goes where. There, all done.

6) oh yeah, I forgot the header... "linear equations"... but it shouldn't be that hard to put equations on this afterwards and get it right.



Post Edited (12-24-03 03:31)

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It's only after we've lost everything, that we are free to do anything.

There was 13 questions and these are the last 4 which i spent a couple of hours doing and couldnt work em out
Thanks for you help!