SOLUTION: Point P (u,v) is in the first quadrant on the graph of the line connecting the points (0,4) and (4,0). A shaded triangular region is shown in the diagram. For what point P will t

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: Point P (u,v) is in the first quadrant on the graph of the line connecting the points (0,4) and (4,0). A shaded triangular region is shown in the diagram. For what point P will t      Log On


   

Question 1152182: Point P (u,v) is in the first quadrant on the graph of the line connecting the points (0,4) and (4,0). A shaded triangular region is shown in the diagram. For what point P will the area of the shaded triangular region be a maximum?
Found 2 solutions by MathLover1, lolxcry:
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

as you can see, point P is midpoint of hypotenuse, and its coordinates are:
P(%280%2B4%29%2F2), (%280%2B4%29%2F2)=(2,2)

a shaded triangular region is right triangle with legs length of 2
so, the area of a shaded triangular region is:
+A=%281%2F2%29%2A2%2A2=%282%2F2%29%2A2=2

Answer by lolxcry(1) About Me  (Show Source):