State whether the two lines in the following are parallel, perpen… - Vidyadip

Question

State whether the two lines in the following are parallel, perpendicular or neither.
Through (6, 3) and (1, 1); through (-2, 5) and (2, -5)

✓

Answer

Slope of line joining (6, 3) and (1, 1)
$\text{m}_1 =\frac{1-3}{1-6}=\frac{-2}{-5}=\frac{2}{5}$
Slope of line joining (-2, 5) and (2, -5)
$\text{m}_2=\frac{\text{5}-{5}}{2-(-2)}=\frac{-10}{4}=\frac{-5}{2}$
Here $\text{m}_1\times\text{m}_2=\frac{2}{5}\times\frac{-5}{2}=-1$
$\therefore$ The lines are perpendicular to each other.

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