SOLUTION: A vertical line divides a triangle with vertices A(0,0), B(9,0) and C(8,4) into two regions of equal area. Find the equation of the line.

Algebra ->  Length-and-distance -> SOLUTION: A vertical line divides a triangle with vertices A(0,0), B(9,0) and C(8,4) into two regions of equal area. Find the equation of the line.      Log On


   

Question 1120892: A vertical line divides a triangle with vertices A(0,0), B(9,0) and C(8,4) into two regions of equal area. Find the equation of the line.
Found 2 solutions by greenestamps, ikleyn:
Answer by greenestamps(13195) About Me  (Show Source):
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The area of the given triangle is one-half base times height: (1/2)(9)(4) = 18. So we want the vertical line to divide the triangle into two pieces each with area 9.

Any point on segment AC will have coordinates of the form (2a,a); the vertical line through (2a,a) will intersect AB at (2a,0).

The area of the triangle formed by the vertical line and point A will have area one-half base times height: (1/2)(2a)(a) = a^2.

Since we want the area of that triangle to be 9, a^2=9 --> a = 3.

Answer: The vertical line has the equation x=3.

Answer by ikleyn(52756) About Me  (Show Source):
You can put this solution on YOUR website!
.
The correct answer is: 

    The vertical line has the equation  x = 6.