# Perpendicular lines in coordinate geometry

#### Jamantha

##### New member

I attempted this question and I got it wrong because apparently l3 is perpendicular to BC. But I really don't understand why this is. Is this simply a mistake in the textbook that I can ignore?

According to the mark scheme all lines intersect at (78/19,140/19) can someone please explain why the lines meet here?

Many thanks for any help

#### Dr.Peterson

##### Elite Member
I attempted this question and I got it wrong because apparently l3 is perpendicular to BC. But I really don't understand why this is. Is this simply a mistake in the textbook that I can ignore?

According to the mark scheme all lines intersect at (78/19,140/19) can someone please explain why the lines meet here?
Why do you say "apparently l3 is perpendicular to BC"? Nothing in the problem says that; if you meant the "mark scheme" says that, please show that to us; but it would be an error.

In your work, why do you say "C(-4, 14)", "A(-2, 2)", and "C(13, 8)"? Are those from a different problem?

Your work otherwise looks good, except that where you say "reciprocal" you should be saying "negative reciprocal".

#### Jamantha

##### New member
Thank you for your response and the feedback, Dr Peterson. Yes according to the mark scheme l3 is perpendicular to BC. Although I cannot see why.

#### Dr.Peterson

##### Elite Member
I think it should be obvious that they just put B wrongly in one place; everything else around it screams A!

They start with AC, accidentally say BC though they use the negative reciprocal of the gradient of AC, and then correctly say the line passes through B.

Don't worry about it. I've seen far worse errors ...