Question
Show that line $A B$ is perpendicular to line $\mathrm{BC}$, where $\mathrm{A}(1,2), \mathrm{B}(2,4)$ and $\mathrm{C}(0,5)$.
✓
Answer
Let slopes of lines $\mathrm{AB}$ and $\mathrm{BC}$ be $m_1$ and $m_2$ respectively.
$
\begin{aligned}
& \therefore m_1=\frac{4-2}{2-1}=2 \text { and } \\
& m_2=\frac{y_2-y_1}{x_2-x_1}=\frac{5-4}{0-2}=-\frac{1}{2}
\end{aligned}
$
Now $m_1 \times m_2=2 \times\left(-\frac{1}{2}\right)=-1$
$\therefore$ Line $\mathrm{AB}$ is perpendicular to line $\mathrm{BC}$.
$
\begin{aligned}
& \therefore m_1=\frac{4-2}{2-1}=2 \text { and } \\
& m_2=\frac{y_2-y_1}{x_2-x_1}=\frac{5-4}{0-2}=-\frac{1}{2}
\end{aligned}
$
Now $m_1 \times m_2=2 \times\left(-\frac{1}{2}\right)=-1$
$\therefore$ Line $\mathrm{AB}$ is perpendicular to line $\mathrm{BC}$.
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