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Use slopes to determine whether the points $A(4,1), B(7,3)$, and $C(3,9)$ are the vertices of a right triangle.
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The slope $m_1$ of line $\overleftrightarrow{A B}$ is $(3-1) /(7-4)=\frac{2}{3}$. The slope $m_2$ of line $\stackrel{B}{B C}$ is $\quad(9-3) /(3-7)=-\frac{6}{4}=-\frac{3}{2}$. angle at $B$.
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