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Start at the origin in the plane. Move one-third of the way toward
the point (9, 12) and then turn
to the left and move 10 units.
What are the coordinates of your final position?
a) 
b) 
c) 
d) 
e) 
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(see sketch) when you turn 
counterclockwise. The equation of the
line, 
, through this point is given by 
. So we need to find all points that are
10 units from 
and intersect 
. That is, we must solve the system
It follows that
It follows that the coordinates of the final position are 
.
Perhaps is might be easier if we notice that the slope of 
is -3∕4 and that a triangle with base equal to 8 and
height equal to 6 has a hypotenuse of length 10. So from 
we move 8 units left and 6 units up (the blue
path).
If you miss this question please review the Pythagorean Theorem. |