Answer:
(0,0), (4, 0) and (0, 12)
Step-by-step explanation:
The equation of the line passing from A and B is given by
y - y1 = m (x - x1)
y - 0 = (-b/a) (x -a)
this lines passes from (2, 3)
So,
3 = - b/a (2 - a)
b = 3a/ (a -2)
Area o the triangle formed
A = 1/2 x base x height
A = 1/2 x a x b
A = 3a² / (2a -4)
Differentiate with respect to a.
[tex]dA/da = \frac{6a(2a-4)-6a^2}{\left (2a-4\right)^{2}}[/tex]
For maxima and minima, dA/da = 0
So, 6a² - 24 a = 0
a = 4
b = 3 x 4 x 4 / (2 x 4 - 4)
b = 48 / 4 = 12
So, the vertices of the triangle is (0,0), (4, 0) and (0, 12).
