Question

Points A(−3, −4), B(−1, 2), C(4, 1) are corners of a triangle. Write down the

equation of a line, passing through A and containing the height (altitude) of this triangle dropped from A. Find the length of this height.

Answer 1

BC has slope 1

so the altitude to BC will have slope -1
Thus, the altitude through A is
y+4 = -1(x+3)
BC has equation
y-2 = 1(x+1)
x-y+3 = 0
The distance from A to BC is
|1(-3)-1(-4)+3|/√(1^2+1^2) = 4/√2 = 2√2