Parallel, Perpindicular or Neither LINE GH AND LINE RS

Question

G(14,13) H (-11,10) R (-3,7) S (-4,-5)?

Answer 1

Let the points on GH : G(x₁, y₁) = (14, 13) and H(x₂, y₂) = (- 11, 10).

Slope (m₁) = [(y₂ - y₁)/(x₂ -x₁)]

m₁ = [(10 - 13)/(- 11 - 14)]

m₁  = [(- 3)/(- 25)]

m₁ = 3/25

⇒ m₁ = 3/25.

Let the points on RS : R(x₁, y₁) = (- 3, 7) and S(x₂, y₂) = (- 4, - 5).

Slope (m₂) = [(y₂ - y₁)/(x₂ -x₁)]

m₂ = [(- 5 - 7)/(- 4 + 3)]

m₂  = - 12/(- 1)

⇒ m₂ = - 12.

Since m₁ is not equals to  m₂ and m₁ is not a negative reciprocal of m₂, the lines GH and RS are neither parallel nor perpendicular.