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)

RedDragon1 Apr 30, 2024

#1**+2 **

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

CPhill Apr 30, 2024