Let L be the line passing through the point P(1,2) such that its intercepted segment betwe…

Question

Let $L$ be the line passing through the point $P(1,2)$ such that its intercepted segment between the coordinate axes is bisected at $P$. If $L_1$ is the line perpendicular to $L$ and passing through the point $(-2,1)$, then the point of intersection of $L$ and $L_1$ is:

Accepted Answer

$L$: intercepts $(2,0),(0,4)$ (since $P(1,2)$ is midpoint): $2x+y=4$.

$L_1$ perpendicular to $L$ (slope $-2$, so $L_1$ has slope $\dfrac12$) through $(-2,1)$:
$$y-1=\frac12(x+2) \implies x-2y=-4$$

Solving $2x+y=4$ and $x-2y=-4$: from the first, $y=4-2x$; substitute: $x-2(4-2x)=-4 \implies 5x=4 \implies x=\dfrac45,\ y=\dfrac{12}5$

Solutions · 1