The equation of the line whose midpoint betwe | vedclass

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Question

(A) Let the line intersect the $x$-axis at $(a, 0)$ and the $y$-axis at $(0, b)$.Since the midpoint of the segment between the axes is $(x_1, y_1)$,we

Vedclass · Accepted Answer

$\frac{x}{x_1} + \frac{y}{y_1} = 2$

Vedclass · Answer

(A) Let the line intersect the $x$-axis at $(a, 0)$ and the $y$-axis at $(0, b)$.Since the midpoint of the segment between the axes is $(x_1, y_1)$,we have:$x_1 = \frac{a+0}{2} \implies a = 2x_1$$y_1 = \frac{0+b}{2} \implies b = 2y_1$The intercept form of the line is $\frac{x}{a} + \frac{y}{b} = 1$.Substituting the values of $a$ and $b$,we get $\frac{x}{2x_1} + \frac{y}{2y_1} = 1$.Multiplying by $2$,we obtain $\frac{x}{x_1} + \frac{y}{y_1} = 2$.

The equation of the line whose midpoint between the axes is $({x_1}, {y_1})$ is:

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