Question

Find the distance between and when: (i) PQ is parallel to the y -axis, (ii) PQ is parallel to the x -axis.

Answer 1

The given points P and Q are ( x 1 , y 1 ) and ( x 2 , y 2 ).

Let, the distance between the two points ( x 1 , y 1 ) and ( x 2 , y 2 ) is d.

The formula for the distance between two points is given by,

d= ( x 2 − x 1 ) 2 + ( y 2 − y 1 ) 2 (1)

(i)

If the line PQ is parallel to the y-axis then the equation of line is given by,

x=C

Where, C is constant.

Each point lies on the line PQ have same x coordinates,

x 1 = x 2 (2)

Substitute the value of x 1 from equation (2) to equation (1).

d= ( x 2 − x 2 ) 2 + ( y 2 − y 1 ) 2 = ( y 2 − y 1 ) 2 =| y 2 − y 1 |

Thus, if the line PQ is parallel to the y-axis the distance between the two points ( x 1 , y 1 ) and ( x 2 , y 2 ) is | y 2 − y 1 |.

(ii)

If the line PQ is parallel to the x-axis then the equation of line is given by,

y=C

Where, C is constant.

Each point lies on the line PQ have same y coordinates,

y 1 = y 2 (3)

Substitute the value of y 1 from equation (3) to equation (1).

d= ( x 2 − x 1 ) 2 + ( y 2 − y 2 ) 2 = ( x 2 − x 1 ) 2 =| x 2 − x 1 |

Thus, if the line PQ is parallel to the x-axis the distance between the two points ( x 1 , y 1 ) and ( x 2 , y 2 ) is | x 2 − x 1 |.