Question

If a line intercepted between the coordinate axes is trisected at a point $A(4, 3)$, which is nearer to $x$-axis, then its equation is :

• A. $4x ?3y = 7$
• B. $3x + 2y = 18$
• C. $3x + 8y = 36$
• D. $x + 3y = 13$

Answer 1

The Correct Option is B

To find the equation of the line intercepted between the coordinate axes and trisected at point \( A(4, 3) \), we follow these steps:

1. Let's assume the equation of the line in the intercept form: \(\frac{x}{a} + \frac{y}{b} = 1\) where a and b are the intercepts on the x-axis and y-axis, respectively.
2. Since point \(A(4, 3)\) is nearer to the x-axis, it is one-third the distance from the x-intercept. Hence, the coordinates of point \(A\) can be given in terms of the intercepts as: \(A = \left( \frac{2a}{3}, \frac{b}{3} \right)\).
3. According to the problem, point \(A(4, 3)\) corresponds to these coordinates. Thus, we have:
   • \(\frac{2a}{3} = 4\) implies \(2a = 12\), so \(a = 6\).
   • \(\frac{b}{3} = 3\) implies \(b = 9\).
4. The line equation in intercept form becomes: \(\frac{x}{6} + \frac{y}{9} = 1\).
5. Convert the intercept form to the standard linear form:
   • Multiply through by 18 (LCM of 6 and 9) to clear fractions: 3x + 2y = 18.
6. Thus, the equation of the line is 3x + 2y = 18.

The correct answer is 3x + 2y = 18.