# 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.

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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.

by (14.7k points)

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.