Assignment:
The diagram below shows a triangle ABC whose vertices are at A (-1, 3), B (6, 5) and C (8, -3). The line BP is perpendicular to the line AC, and M is the midpoint of BC.
Note that BP is called an altitude of triangle ABC and that AM is called a median of triangle ABC.
a) Find the gradient of
i) The line AC
ii) The altitude BP
(Show answers as a fraction in its simplest form)
b) Find the equation of the altitude BP, expressing your answer in the form
y = mx + c
c) Find the coordinates of M.
d) Find the equation of the median AM, expressing your answer in the form
y = mx + c
e) Explain how you would find the coordinates of the point of intersection of the altitude BP and the median AM.
Provide complete and step by step solution for the question and show calculations and use formulas.