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# Coordinate geometry watch

1. Just need a little clearing up:

I have done the following question but part c I got a little confused about because I done a different method and ended up with the wrong answer even though that same method has worked for other questions - and I am just a little worried because I thhought that regardless of what method you use you should still get the same answer. So I am hoping that I have just got confused over a negative sign or something!

The points A and B have coordinates (4,6) and (12,2) respectively.

The straight line l1 passes through A and B.

a) Find an equation for l1 in the form ax + by = c, where a, b and c are integers.

The straight line l2 passes through the origin and has gradient -4.

b) Write down an equation for l2.

The lines l1 and l2 intercept at the point C.

c) Find the exact coordinates of the mid-point of AC.

So for part c:

I got the l1 has an equation of : x + 2y - 16 and l2 has an equation of: y = -4x

Anyway - instead of spotting the easier method of substituting l1 into l2 I equated the two equations together to make:

-4x = -1/2x +8

7/2 x = 8

x = 16/7

Therefore y = - 64/7

so when I used thses coordinates I got the wrong midpoint.

The answers for the c using the substituiton method should be :

x = -16/7

y = 64/7

and then using these coordinates I get the right midpoint

Anyway - basically I know I musta gone wrong somewhere with my original method but I just cant see where - because as far as I am concerned it shouldnt matter what method I use, even though mine is slighly more complicated - I should still get the right answer??
2. (Original post by christinajane)
Just need a little clearing up:

I have done the following question but part c I got a little confused about because I done a different method and ended up with the wrong answer even though that same method has worked for other questions - and I am just a little worried because I thhought that regardless of what method you use you should still get the same answer. So I am hoping that I have just got confused over a negative sign or something!

The points A and B have coordinates (4,6) and (12,2) respectively.

The straight line l1 passes through A and B.

a) Find an equation for l1 in the form ax + by = c, where a, b and c are integers.

The straight line l2 passes through the origin and has gradient -4.

b) Write down an equation for l2.

The lines l1 and l2 intercept at the point C.

c) Find the exact coordinates of the mid-point of AC.

So for part c:

I got the l1 has an equation of : x + 2y - 16 and l2 has an equation of: y = -4x

Anyway - instead of spotting the easier method of substituting l1 into l2 I equated the two equations together to make:

-4x = -1/2x +8

7/2 x = 8

x = 16/7

Therefore y = - 64/7

so when I used thses coordinates I got the wrong midpoint.

The answers for the c using the substituiton method should be :

x = -16/7

y = 64/7

and then using these coordinates I get the right midpoint

Anyway - basically I know I musta gone wrong somewhere with my original method but I just cant see where - because as far as I am concerned it shouldnt matter what method I use, even though mine is slighly more complicated - I should still get the right answer??
I haven't had time to look over but i'm sure drawing a diagram would help clear things up?
3. (Original post by christinajane)
...
7/2 x = 8.

Where did this line come from?
4. (Original post by christinajane)
J
-4x = -1/2x +8

7/2 x = 8
You made an error in going from the first quoted line to the second. Have another go.

Edit: Too slow
5. (Original post by ghostwalker)
You made an error in going from the first quoted line to the second. Have another go.

Edit: Too slow
Ahhh yeah!! Thank you - I knew it was gonna be something silly like those pesky negative signs and me not remembering that I have moved something across the = sign!

Sometimes I just need someone else to look at these things because I just couldnt see it when I went over it again but yeah it should be

7/2x = -8

Then it would all work out, even with my slightly more complicaed method.

Thanks guys!

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Updated: May 2, 2016
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