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 $(5, 6)$ and $(2, 3)$; through $(9, -2)$ and $(6, -5)$

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Answer

Slope of line joining $(5, 6)$ and $(2, 3)$
$\text{m}_1=\frac{\text{y}_2-\text{y}_1}{\text{x}_2-\text{x}_1}=\frac{3-6}{2-5}=\frac{-3}{-3}=1$
Slope of line joining $(9, -2)$ and $(6, -5)$
$\text{m}_2=\frac{\text{y}_2-\text{y}_1}{\text{x}_2-\text{x}_1}=\frac{-5-(-2)}{6-9}=\frac{-5+2}{-3}=1$
Here $m_1 = m_2$
$\therefore$ The two lines are parallel.

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