How to attempt finding unknown y coord in a triangle

question b) is the one I do not know how to approach. I know I could probably use pythagoras, but I predict that the calculations will get a little bit messy. There are other ways to complete this on the mark scheme, like "gradient LM * gradient MN", but I don't understand where they're coming from.

any help pls?

If (and only if) two lines are perpendicular, the product of their gradients is -1. (You can prove this using vectors).
Thus gradient LM = (-4-2)/(7+1) = -6/8 = -3/4, and gradient MN = (p+4)/(16-7) = (p+4)/9.
Since angle LMN = 90 degrees, LM is perpendicular to MN.
Thus -3/4 * (p+4)/9 = -1 -> 3(p+4)/36 = 1 -> p+4 = 12 -> p=8.

Okay, thank you, I get that.

What about part c)? I know the answer is 2 + p + 4, but I'm not sure why?

Does this help at all:

That's how I illustrated it to myself at the start, but I still can't see why you'd add the present 3 y-coords (+ ignore the minus sign at M (7, -4)?).

Would it help if you think about it as vectors? (start from M, add the vector MN then add the vector -ML)