Answer:
3x - 4y = 0
Step-by-step explanation:
The triangle Δ ABC has vertices A(0,0), B(0,4) and C(3,0).
Therefore, the equation of the straight line BC in intercept form will be
[tex]\frac{x}{3} + \frac{y}{4} = 1[/tex]
⇒ 4x + 3y = 12
⇒ [tex]y = - \frac{4}{3}x + 4[/tex] .......... (1)
This is a equation in slope-intercept form and the slope is [tex]- \frac{4}{3}[/tex].
Now, the altitude AR is perpendicular to equation (1) and hence its slope will be [tex]\frac{3}{4}[/tex].
{Since, the product of slope of two mutually perpendicular straight line is always - 1}
Therefore, the equation of the altitude AR which passes through A(0,0) will be
[tex]y = \frac{3}{4}x[/tex]
⇒ 4y = 3x
⇒ 3x - 4y = 0 (Answer)
