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Triangle ABC has vertices A(0, 8), B(2, 0),C(8, 0). A line through B cuts the area of \(\triangle ABC\) in half; find the sum of the slope and y-intercept of this line.

 Dec 13, 2018
 #1
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The height of ABC =   8

 

The midpoint of   (2,0) and (8,0)   =   (5,0)

 

And the line  connnecting   (0,8) and (5,0)   will  divide the area of the orginal triangle in half

 

The slope  of this line  is    [ 8 - 0 ] / [ 0 - 5 ]  =  8 / -5  = -8/5

 

The equation of this line is

 

y = - (8/5)x + 8

 

The y intercept  = 8

 

So....the sum of the slope and y intercept  =  -8/5 + 8  =  32 / 5

 

Here's a graph :

 

 

 

cool cool cool

 Dec 13, 2018
edited by CPhill  Dec 14, 2018
 #2
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But the line should be through B

Guest Dec 14, 2018

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