I attempted this question and I got it wrong because apparently l_{3} 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 l

_{3} 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".