Question

Find the distance between P(x₁, y₁) and Q(x₂, y₂) when 

(i) PQ is parallel to the y-axis 

(ii) PQ is parallel to the x-axis.

Answer 1

Key points to solve the problem: 

• Idea of distance formula- Distance between two points A(x₁,y₁) and B(x₂,y₂) is given by- AB = \(\sqrt{x_2 - x_1)^2 + (y_2 - y_1)^2}\) 

Given, P(x₁, y₁) and Q(x₂, y₂) are two points. 

i) When PQ is parallel to y-axis This implies that x – coordinate is constant 

⇒ x₂ = x₁ 

∴ from distance formula: 

PQ = \(\sqrt{(x_2 - x_1)^2 + (y_2-y_1)^2}\) = \(\sqrt{0 + (y_2 + y_1)^2}\) = |y₂ - y₁| 

ii) When PQ is parallel to x-axis This implies that y – coordinate is constant 

⇒ y₂ = y₁ 

∴ from distance formula: 

PQ = \(\sqrt{(x_2 - x_1)^2 + (y_2-y_1)^2}\) =\(\sqrt{0 + (x_2 + x_1)^2}\) = |x₂ - x₁| 

Note: we take modulus because square root gives both positive and negative values but distance is always positive so we make it positive using modulus function.