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??