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.
+128474 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 :
