-- Driving at 30 mph for 20 minutes (1/3 hour), you cover 10 miles.
-- Walking at 3 mph for 10 minutes (1/6 hour), you cover 0.5 mile.
-- Average speed = (total distance covered) / (time to cover the distance)
= (10.5 miles) / ( 1/2 hour)
= 21 miles per hour.
When you have a point A and then transform it using a linear transformation (like rotation, reflections, etc.), we mark it as A' to say, "This is the point which corresponds to A after the transformations were applied". This establishes a link between the two, even though they may appear to be unrelated to someone looking at the graph.
