(4A-4)

Recall that the plane shaded in pink has the equation 

z = -x - 2y

The line shown in white is x=y, in the plane z=0. 

The line shown in yellow is the line in the pink plane which points in the direction x = y 

In this exercise lets use (x,y) coordinates. So, point 0 is the origin, (0,0). Point A is (0,-2) and point B is (-2,-2).

①  What is the distance 0B ?

②  Point C is the point on the pink plane where x = y = -2.  What is the distance BC?

③ What, therefore, is the gradient of the yellow line, which is the slope of the plane z = -x - 2y, in the direction x = y ?