Question:
<p>If a straight line passing through the point P(- 3, 4) is such that its intercepted portion between the coordinate axes is bisected at P, then its equation is</p>
<p style="display:inline">4x + 3y = 0</p>
<p style="display:inline">3x - 4y + 25 = 0</p>
<p style="display:inline">4x - 3y + 24 = 0</p>
<p style="display:inline">x - y + 7 = 0</p>
Step-by-Step Solution
Key Concept: Use the intercept form of a line x/a + y/b = 1, where the midpoint of the segment between the axes (a, 0) and (0, b) is given by (a/2, b/2).
<p>Let the equation of required line having intercepts a and b with the axes is <span class="math-tex">$\frac{x}{a}+\frac{y}{b}=1$</span> ...(i)<br />
<img alt="" data-imgur-src="qxs4yXG.png" src="https://media-mycbseguide.s3.amazonaws.com/images/imgur/qxs4yXG.png" style="width: 150px; height: 146px;" /><br />
Now, according to given information, P is the mid-point of AB<br />
<span class="math-tex">$\therefore \quad P=\left(\frac{a}{2}, \frac{b}{2}\right)=(-3,4)$</span> [given]<br />
<span class="math-tex">$\Rightarrow$</span> (a, b) = (-6, 8)<br />
On putting the value of a and bin Eq. (i), we get<br />
<span class="math-tex">$\frac{x}{-6}+\frac{y}{8}=1 \Rightarrow$</span> 8x - 6y = - 48<br />
<span class="math-tex">$\Rightarrow$</span> 4x - 3y + 24 = 0</p>
Correct Answer: C