+2668 I answered the same question here: https://web2.0calc.com/questions/coordinates_83752#r2
+23252 The area of the triangle is: A = ½ · (base) · (height) = ½ · ( 7 ) · ( 3 ) = 21/2
The equation of line(BA) is: y = (3/10)(x + 6).
The line x = k is a vertical line that passes through the x-intercept (k, 0).
It also passes through the point ( k, (3/10)(k + 6) ) on the line(BA).
The region of the triangle to the left of the line x = k is a triangle with base length = k + 6
and whose height is (3/10)(k + 6).
The area of this triangle is: ½ · (k + 6) · (3/10)(k + 6)
Since this area = one-half of the total area of the triangle:
½ · (k + 6) · (3/10)(k + 6) = ½ · (21/2)
(3/10)(k + 6)2 = 21/2
(k + 6)2 = 35
k + 6 = sqrt(35) (you can ignore the other answer)
k = sqrt(35) - 6 (a point slightly to the left of the axis)
