Question

The vertices of the triangle ABC are (-2,1),(5,4) and (2,-3) respectively. Find the length of the altitudE through A.

Answer 1

Dear student
$$\begin{gathered} -2,15,42,-3 \\ \mathrm{Let}\mathrm{AB}\mathrm{be}\mathrm{the}\mathrm{altitude}\mathrm{from}\mathrm{vertex}\mathrm{A}\mathrm{and}\mathrm{m}\mathrm{be}\mathrm{the}\mathrm{slope}\mathrm{of}\mathrm{AE} \\ \mathrm{Then}\mathrm{AE}\perp \mathrm{BC}\Rightarrow \mathrm{Slope}\mathrm{of}\mathrm{AE}\times \mathrm{Slope}\mathrm{of}\mathrm{BC}=-1 \\ \Rightarrow \mathrm{m}\times \frac{-3-4}{2-5}=-1 \\ \Rightarrow \mathrm{m}\times \left(\frac{-7}{-3}\right)=-1 \\ \Rightarrow \mathrm{m}=\frac{-3}{7} \\ \mathrm{Since}\mathrm{AE}\mathrm{passes}\mathrm{through}\mathrm{A}\left(-2,1\right).\mathrm{So},\mathrm{its}\mathrm{equation}\mathrm{is} \\ \mathrm{y}-1=\frac{-3}{7}\left(\mathrm{x}+2\right) \\ \Rightarrow 7\mathrm{y}-7=-3\mathrm{x}-6 \\ \Rightarrow 3\mathrm{x}+7\mathrm{y}-1=0 \end{gathered}$$
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