three equations for one answer!

okay this is going to be short, random post about maths last night! so, valerie called me last night to talk about Amaths. so we happen to stumble on this geomertry question.

well! valerie got me onto the question, so i was determined to get the answer >:( right, so i came up with 3 equations. i worked my brain so hard, squeezed every drop of my brain juice into this question. so i came up with 3 equations. and no matter what i did, the answer was 6! it did not match with the Q(9,7) which was the answer. i stared at the paper, exercising my brain in the middle of the night trying to figure out where i have gone wrong.

then valerie kept telling me to give up, oh knowing myself, i dont really give up until i get really really exhausted and desperate. so i kept working on that single part of the question. i felt like a scientist, trying to go back and forth coming up with more equations and formula to find one answer. okay, so i got very annoyed. then my mother came to tell me to do it another day. so i had no choice but to go to sleep. then just as i was making my way to the bathroom, something hit my mind. the reason why i wasnt able to get any answer close to Q(9,7) from 3 different sets of equations, was because i was supposed to use the midpoint of PQ! well i believed it was a little late to go back since ive gotten so tired being angry with the question. so i messaged valerie and went to sleep. haha, hope she got the answer somehow?