+0  
 
0
50
1
avatar

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 = ?

 Jan 31, 2021
 #1
avatar+116126 
+1

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 ]

 

 

cool cool cool

 Jan 31, 2021

50 Online Users

avatar
avatar
avatar
avatar
avatar
avatar
avatar