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)

✓

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 m₁ = m₂
$\therefore$ The two lines are parallel.

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