Question

please refer to the pic below :​

Answer 1

Answer: C = $\rm ( \dfrac{40}{b} , 0)$

Explanation:

We know,

$\rm \Delta = \dfrac{1}{2} | x_1 (y_2 - y_3) + x_2 (y_3 - y_1) + x_3 (y_1 - y_2) |$

Now, A is the origin as both the axes meet each other.

So, $\rm x_1 = y_1 = 0$. (Coordinates are 0,0)

∴ $\rm \dfrac{1}{2} | 0(y_2 - y_3) + x_2(y_3 - 0) + x3(0 - y2) | = 20$

=> $\rm | x_2(y_3) + x_3(- y_2) | = 20 \cdot 2$

=> $\rm | ay_3 - bx_3 | = 40$

Now, as C lies in X axis, then y = 0.

=> $\rm | - bx_3 | = 40$

=> $\rm bx_3 = 40$

=> $\rm x_3 = \dfrac{40}{b}$.

More:

In a right ∆, whenever there is an altitude to the hypotenuse from its opposite vertex, and hypotenuse = p + q, then the length of altitude is given by:

$\rm h^2 = pq$.

(See attachment.)