# Find the distance between the points A(x1, y1) and B(x2, y2), when (i) AB is parallel to the x-axis (ii) AB is parallel to the y-axis

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Find the distance between the points A(x1, y1) and B(x2, y2), when

(i) AB is parallel to the x-axis

(ii) AB is parallel to the y-axis

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(i) Given: AB is parallel to the x - axis.

When AB is parallel to the x - axis, the y co - ordinate of A and B will be the same.

i.e., y1 = y2

Distance

$\sqrt{(x_2-x_1)^2+(y_1+y_1)^2}$

⇒ |x2 – x1|

Therefore the distance between A and B when AB is parallel to x - axis is |x2 – x1|

(ii) Given: AB is parallel to the y - axis.

When AB is parallel to the y - axis, the x co - ordinate of A and B will be the same.

i.e., x2 = x1

Distance

$\sqrt{(x_1-x_1)^2+(y_2+y_1)^2}$

⇒ |y2 – y1|

Therefore the distance between A and B when AB is parallel to y - axis is |y2 – y1|