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

1.	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
Answer» (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\|

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

Answer»

(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|