# Cordinate geometry

• Mar 9th 2008, 01:49 AM
Coach
Coordinate geometry
Dear forum members,

could you please check if my calculations are correct, I have tried several times, I alway keep getting the wrong answer though.

Problem

Find the values for k for which the lines $\displaystyle 2x+ky-11=0$ and $\displaystyle (3-k)x+y+2=0$are perpendicular.

My solution

$\displaystyle -3x+kx= \frac{k}{2x}$
-3x+kx and 2x have to be the same

so $\displaystyle -3x+kx= 2x$

I always keep getting 5 or 1 as the answer for k, is it correct?

Thank you in advance!
• Mar 9th 2008, 01:54 AM
mr fantastic
Quote:

Originally Posted by Coach
Dear forum memebers,

could you please check if my calculations are correct, I have tried several times, I alway keep getting the wrong answer though.

Problem

Find the values for k for which the lines $\displaystyle 2x+ky-11=0$ and $\displaystyle (3-k)x+y+2=0$are perpendicular.

My solution

$\displaystyle -3x+kx= //frac{k}{2x}$
the bottom numbers have to be the same

so $\displaystyle -3x+kx= 2x$

I always keep getting 5 or 1 as the anwer for k, is it correct?

Thank you in advance!

Two lines are perpendicular if the product of their gradients is equal to -1.

$\displaystyle 2x+ky-11=0 \Rightarrow y = \frac{-2x+11}{k} \Rightarrow m = -\frac{2}{k}$.

$\displaystyle (3-k)x+y+2=0 \Rightarrow y = -(3 - k)x - 2 = (k - 3)x - 2 \Rightarrow m = k - 3$.

Therefore you require $\displaystyle \left( -\frac{2}{k} \right) \, (k-3) = -1 \Rightarrow -2(k-3) = -k \Rightarrow k = 6$.
• Mar 9th 2008, 01:59 AM
Coach
Thank you so much!

I would not have been able to do that on my own.
• Mar 9th 2008, 03:02 AM
mr fantastic
Quote:

Originally Posted by Coach
Dear forum members,

could you please check if my calculations are correct, I have tried several times, I alway keep getting the wrong answer though.

Problem

Find the values for k for which the lines $\displaystyle 2x+ky-11=0$ and $\displaystyle (3-k)x+y+2=0$are perpendicular.

I always keep getting 5 or 1 as the answer for k, is it correct?

Thank you in advance!

I just realised that if you kept getting 5 plus 1 as the answer for k it would be correct (Rofl)
• Mar 9th 2008, 03:06 AM
mr fantastic
Quote:

Originally Posted by Coach
Thank you so much!

I would not have been able to do that on my own.

I'm sure you would (Yes) You've just got to work through each link in the chain.