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(B) Let the line be $\frac{x}{a} + \frac{y}{b} = 1.$ Since the line passes through $P(-3, 4)$ and this point bisects the intercepted portion between t

Vedclass · Accepted Answer

$4x-3y+24=0$

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(B) Let the line be $\frac{x}{a} + \frac{y}{b} = 1.$ Since the line passes through $P(-3, 4)$ and this point bisects the intercepted portion between the axes,the coordinates of the intercepts are $A(a, 0)$ and $B(0, b).$ By the midpoint formula,$P = \left( \frac{a+0}{2}, \frac{0+b}{2} \right) = \left( \frac{a}{2}, \frac{b}{2} \right).$ Given $P(-3, 4),$ we have $\frac{a}{2} = -3 \implies a = -6$ and $\frac{b}{2} = 4 \implies b = 8.$ Substituting these values into the intercept form equation: $\frac{x}{-6} + \frac{y}{8} = 1.$ Multiplying by $24,$ we get $-4x + 3y = 24,$ or $4x - 3y + 24 = 0.$

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

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