SOLUTION: Find the equation of the straight line through A(1,4) which is perpendicular to the line passing through the points B(2,-2) and C(4,0). Hence find the area of the triangle ABC, giv

Algebra ->  Formulas -> SOLUTION: Find the equation of the straight line through A(1,4) which is perpendicular to the line passing through the points B(2,-2) and C(4,0). Hence find the area of the triangle ABC, giv      Log On


   

Question 879934: Find the equation of the straight line through A(1,4) which is perpendicular to the line passing through the points B(2,-2) and C(4,0). Hence find the area of the triangle ABC, giving your answer in the simplest possible form
Answer by josgarithmetic(39618) About Me  (Show Source):
You can put this solution on YOUR website!
Line BC

%280-%28-2%29%29%2F%284-2%29=1, the slope.
b=y-mx
b=-2-1%2A2
b=-4
highlight_green%28y=x-4%29.

Length BC
sqrt%28%282-4%29%5E2%2B%28-2-0%29%5E2%29
sqrt%284%2B4%29
sqrt%288%29
highlight_green%28BC=2sqrt%288%29%29

Line containing A and perpendicular to line BC
Want slope -1.
Line%2C+y-4=-1%28x-1%29
y-4=-x%2B1
highlight%28y=-x-3%29, one of the answers.

Point of intersection these two lines
x-4=-x-3
2x-4=-3
2x=4-3
2x=1
x=1%2F2
-
Either equation line, y=-x-3
y=-1%2F2-6%2F2
y=-7%2F2
Point on line BC, containing A is (1/2, -7/2).

What next?
Find the distance from A(1,4) to (1/2, -7/2), call the distance AP.
Find the area of the triangle ABC using highlight%28%281%2F2%29BC%2AAP%29.