From the Figure :
Point A is (-3 , -3)
Point B is (6 , 6)
We know that, The Mid Point of Two Points (x₁ , y₁) and (x₂ , y₂) is given by :
![\mathsf{\implies [(\frac{x_1 + x_2}{2})\;,\;(\frac{y_1 + y_2}{2})]}](https://tex.z-dn.net/?f=%5Cmathsf%7B%5Cimplies%20%5B%28%5Cfrac%7Bx_1%20%2B%20x_2%7D%7B2%7D%29%5C%3B%2C%5C%3B%28%5Cfrac%7By_1%20%2B%20y_2%7D%7B2%7D%29%5D%7D)
![\mathsf{\implies Midpoint\;of\;Line\;AB\;is\;[(\frac{-3 + 6}{2})\;,\;(\frac{-3 + 6}{2})]}](https://tex.z-dn.net/?f=%5Cmathsf%7B%5Cimplies%20Midpoint%5C%3Bof%5C%3BLine%5C%3BAB%5C%3Bis%5C%3B%5B%28%5Cfrac%7B-3%20%2B%206%7D%7B2%7D%29%5C%3B%2C%5C%3B%28%5Cfrac%7B-3%20%2B%206%7D%7B2%7D%29%5D%7D)
![\mathsf{\implies Midpoint\;of\;Line\;AB\;is\;[(\frac{3}{2})\;,\;(\frac{3}{2})]}](https://tex.z-dn.net/?f=%5Cmathsf%7B%5Cimplies%20Midpoint%5C%3Bof%5C%3BLine%5C%3BAB%5C%3Bis%5C%3B%5B%28%5Cfrac%7B3%7D%7B2%7D%29%5C%3B%2C%5C%3B%28%5Cfrac%7B3%7D%7B2%7D%29%5D%7D)

For an example 3/5 is like i ate 3 of the 5 apples i had
We'll use the notation
for the principal value and
for all the values:

Part I


Part II. In our range we can write


Part III.

Part IV.


BEHJEJEBEHRUUE what is this eheujrf
Answer:
See the attached figure which represents the problem.
As shown, AA₁ and BB₁ are the altitudes in acute △ABC.
△AA₁C is a right triangle at A₁
So, Cos x = adjacent/hypotenuse = A₁C/AC ⇒(1)
△BB₁C is a right triangle at B₁
So, Cos x = adjacent/hypotenuse = B₁C/BC ⇒(2)
From (1) and (2)
∴ A₁C/AC = B₁C/BC
using scissors method
∴ A₁C · BC = B₁C · AC