A(4;3) B(11;4) C(7;8) y – 3 = x – 4 4 – 3 11 – 4 y – 3 = x – 4 1 7 7(y – 3) = x – 4 7y – 21 – x + 4 = 0 -x + 7y – 17 = 0 x – 7y + 17 = 0 h_c = 1 / √(7^2 + (-1)^2) * |7(5) + (-1)(8) + 17| = 1 / √50 * |35 – 8 + 17| = 1 / √50 * 32 = 32 / √50 = 32 / 5√2 = 5√2 / 5√2 * 32 / 5√2 = 32√2 / 10 = 16√2 / 5
r_A:
y – 3/5 = x – 4/7
y – 3/5 = 3/5
x – 4/7 = 4/7
3(y – 3/5) = 5(x – 4/7)
3y – 9/5 = 5x – 20/7
-5x + 3y – 9/5 + 20/7 = 0
5x – 3y + 9/5 – 20/7 = 0
5x – 3y – 11 = 0
h_B = [5(4) – 3(4) – 11] / √(5² + (-3)²) = [20 – 12 – 11] / √(25 + 9) = [-3] / √34 = -3/√34 = 16/17 * √34
r_B:
y – 8/4 = x – 7/4
y – 8/4 = 4/4
x – 7/4 = 4/4
-y + 8 = x – 7
-x – y + 8 + 7 = 0
-x – y + 15 = 0
x + y – 15 = 0
h_A = |1(4) + 1(3) – 15| / √(1² + 1²)
= |4 + 3 – 15| / √2
= |8| / √2
= 8√2 / 2
= 4√2 = √32