Question

How to calculate part b and c of this question??

Answer 1

For part a, while you didn't ask about this particular part, the equation you should have found is $3x+4y-5=0$.\

For part b, we are given that ∠M = 90°. Recall that perpendicular lines join at a right angle by definition, and that the slope of a perpendicular line is the negative reciprocal slope
$m_{perp}= \dfrac{-1}{m}$.
Using the slope from part a, $m= \frac{-3}{4}$, so $m_{perp}= \frac{4}{3}$.
We can write the equation of the line through M and N as $y+4= \frac{4}{3}(x-7)$.
We are trying to fine the value p for which x is 16, so we substitute 16 into the equation we just found and solve for y (which is p).
$y+4= \frac{4}{3}(16-7)= 12-4=8=p$
$p=8$

For part c, $y=p+6=14$.