Question

Consider the triangle A(4,0), B(-2,4), C(0,6)
What will be the equation of the altitude BM?

Answer 1

BM: y = (2/3) x + 16/3 with segment length of 2.77

Explanation:

AC formula: m = (6-0)/(0-4) = -3/2

(y-0)/(x-4) = -3/2 y = (-3/2)x + 6 ... (1)

BM slope: BM⊥ AC m = 2/3

BM formula: (y-4) / (x- -2) = (y-4) / (x+2) = 2/3

y-4 = 2/3 x + 4/3

y = (2/3) x + 16/3 ... (2) -2≤x≤0.31

intercept of AC and BM (M) from (1) and (2): (-3/2)x + 6 = (2/3) x + 16/3

(13/6) x = 2/3 x = (2/3) / (13/6) = 4/13 ≈ 0.31

y = (2/3) (4/13) + (16/3) = (8/39) + (208/39) = 216/39 = 72/13 ≈ 5.54

M (4/13 , 72/13) or (0.31 , 5.54)

segment BM = √(4/13 - -2)² + (72/13 - 4)² = √1300/169 = 2.77