Question

Show that the line joining the points A (4,8) and B (5, 5) is parallel to the line joining the points C (2, 4) and D (1 ,7).

Answer 1

Proof : 

Slope of line AB = (y₂ - y₁)/(x₂ - x₁)

= (5 - 8)/(5 - 4) = -3

Slope of line CD  = (y₂ - y₁)/(x₂ - x₁)

= (7 - 4)/(1 - 2) = -3

∴ Slope of line AB = Slope of line CD Parallel lines have equal slope. 

∴ line AB || line CD