Question
Prove that if a line $L_{1}$ with slope $m_{1}$ is perpendicular to a line $L_{2}$ with slope $m_{2},$ then $m_{1} m_{2}=-1$
Step 1
This means that if the slope of line $L_{1}$ is $m_{1}$, then the slope of line $L_{2}$, which is perpendicular to $L_{1}$, is $-1/m_{1}$. Show more…
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Prove that if a line $L_{1}$ with slope $m_{1}$ is perpendicular to a line $L_{2}$ with slope $m_{2}$, then $m_{1} m_{2}=-1$. Hint: Refer to the following figure. Show that $m_{1}=b$ and $m_{2}=c .$ Next, apply the Pythagorean Theorem to triangles $O A C, O C B,$ and $O B A$ to show that $1=-b c$.
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