Question
Without using Pythagoras theorem, show that the points A(0, 4), B(1, 2) and C(3, 3) are the vertices of a right angled triangle.
✓
Answer
Slope of $\text{AB}=\frac{2-4}{1-0}=-2$
Slope of $\text{BC}=\frac{3-2}{3-1}=\frac{1}{2}$
slope of AB × slope of BC $=-2\times\frac{1}{2}=-1$
$\therefore$ Anlgle between AB and BC $=\frac{\pi}{2}$
$\therefore$ ABC are the vertices of a right angled triangle.
Slope of $\text{BC}=\frac{3-2}{3-1}=\frac{1}{2}$
slope of AB × slope of BC $=-2\times\frac{1}{2}=-1$
$\therefore$ Anlgle between AB and BC $=\frac{\pi}{2}$
$\therefore$ ABC are the vertices of a right angled triangle.
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