(4A-4)
① Since A is (0,-2) and B is (-2,-2), distance 0A =2 and distance AB = 2.
Therefore, using Pythagoras' theorem, distance 0B = √(22 + 22) = 2√2.
② Since the equation of the plane is z = -x - 2y, the z coordinate at point C is given by z = 2 + 4 = 6.
Therefore distance BC = 6.
③ The gradient of the yellow line is the ratio of the distances, BC/B0 = 6 / 2√2 = 3/√2. Since the change in z is an increase but the changes in x and y are negative, this is a negative gradient:
So the slope of the plane in the direction x = y is equal to -3/√2.