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

Given:

Two points are 
P(x₁, y₁) and Q(x₂, y₂) 

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(i) When PQ is parallel to the y-axis

If PQ is parallel to the y-axis, then 
x₁ = x₂

Distance between P and Q is the difference of their y-coordinates:

\(PQ = |y_2 - y_1|\)

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

If PQ is parallel to the x-axis, then 
y₁ = y₂

Distance between P and Q is the difference of their x-coordinates:

\(PQ = |x_2 - x_1|\)

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Final Answer:

(i) If PQ ∥ y-axis, then 
\(PQ = |y_2 - y_1|\)

(ii) If PQ ∥ x-axis, then 
\(PQ = |x_2 - x_1|\)