Question

37. ABC has vertices A(0, 0) , B(0, 4) , and C(3, 0) . Write the equation for the line containing the altitude overline AR in standard form

Answer 1

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  

$\frac{x}{3} + \frac{y}{4} = 1$

⇒ 4x + 3y = 12

⇒ $y = - \frac{4}{3}x + 4$ .......... (1)

This is a equation in slope-intercept form and the slope is $- \frac{4}{3}$.

Now, the altitude AR is perpendicular to equation (1) and hence its slope will be $\frac{3}{4}$.

{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  

$y = \frac{3}{4}x$

⇒ 4y = 3x

⇒ 3x - 4y = 0 (Answer)