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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.

 Apr 19, 2019
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Find the midpoint of  AC  = (4,4)....let this be D

Now triangle ABD  is under the same height as triangle BCD....and their bases are equal

So  triangle BD divides triangle ABC in half

 

And the line  through BD  has a slope of [4 - 0 ] / [ 4 - 2 ] = 4/2  = 2

 

The equation of this line is

 

y = 2 (x - 2)  =   2x - 4

 

So...the y intercept  =  - 4

 

Here's a pic :

 

 

 

 

cool cool cool

 Apr 19, 2019

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