Answer:
endpoint is (29, -13)
Step-by-step explanation:
Formula for midpoint is 
So, let 
be the coordinates of the endpoint you are looking for.
and 
= (10, -3)
-9 + 
= 20 7 + 
endpoint is (29, -13)
Make a proportion
81/30 = x/600
600/30 = 20
x/81 = 20
x = 1620
Solution: 1620 calories
One way to do it is with calculus. The distance between any point
on the line to the origin is given by
Now, both
and
attain their respective extrema at the same critical points, so we can work with the latter and apply the derivative test to that.
Solving for
, you find a critical point of
.
Next, check the concavity of the squared distance to verify that a minimum occurs at this value. If the second derivative is positive, then the critical point is the site of a minimum.
You have
so indeed, a minimum occurs at
.
The minimum distance is then
