A vertical line divides the triangle with vertices (0,0), (1,1) and (9,1) in the coordinate plane into two regions of equal area. The equation of the line is x = ?
+128408 See the following :
Let A = (0,0) B =(1,1) and C = ( 9,1)
The area of this triangle is (1/2) (1) ( 8) = 4
The line segment connecting AC has a slope of 1/9
Considering our vertical line, the height of the triangle created by this line will be h and the base = (1/9)h
And h will be the horizontal distance from (1,9)
So we have that 1/2 of the area = 2 ....so.....
2 = (1/2) h (1/9)h
2 = h^2 / 18
36 = h^2
6 = h
So x = (9 - 6) = 3 is the vertical line we need
Check
The height of this triangle CDG will be = 6 and the base = (1/9) (6) = 2/3
So....the area = (1/2) (6) (2/3) = 12/ 6 = 2 = 1/2 of [ ABC ]
