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)

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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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