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The line x=k bisects the area of triangle ABC. Find the value of k. A on the coodinate grid is (3,2), B is (-5,0), and C is (1,0)

 Apr 30, 2024
 #1
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Thae area of the triangle =  6

 

The slope of the line between A, B =  [2-0] / [ 3- - 5] =  2 / 8 =  1/4

 

The equation of this line through this segmemt  is

 

y = (1/4)(x + 5)   

 

Let the distance between  -5   and  the x we are looking for  =  x - -5 =  x + 5

 

And the distance between the x axis and AB  is just the eqation of our line

 

So....we need to solve this

 

(1/2) area of triangle ABC  =  (1/2)  ( x + 5) ( 1/4) (x + 5)

 

3 =  (1/8) ( x + 5)^2

 

24  = (x + 5)^2        take the positve root

 

sqrt (24)  = x + 5

 

x =  sqrt (24) - 5     

 

x = 2sqrt (6)  - 5    =   k 

 

cool cool cool

 Apr 30, 2024

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