Question

I have a triangle in a coordinate system(not native english) i have these three points.
A: 4,-2
B:-2,-1
C: 4,3
How do i get the height of it in relation BC?
And, how do i calculate the total area of the triangle?

Made this atm:

AB:
((-2)-4)/((-1)-2) = 2;
y-2=2(x-1)
y = 2*x;
BC:
(4+2)/(3+1) = 3/2;
y-2 = 3/2*(x-1);
y = (3/2)*x+1/2;

Took explanation out, it is in another language ;)

Answer 1

If you were finding slope, then you have it upside down.
slope AB = (-2 + 1)/(4+2) = -1/6

slope of BC = (3+1)/(4+2) = 4/6 = 2/3
equation of BC
y-3 = (2/3)(x-4)
3y - 9 = 2x - 8
2x - 3y + 1 = 0

distance from A(4,-2) to BC
= |2(4) - 3(-2) + 1|√(2^2 + (-3)^2)
= 15/√13