Question

prove that the line through 0, 0 and 2, 3 is parallel to the line through 2, - 2 and 6, 4

Answer 1

Find the gradient of the line that passes through (0,0) and (2,3)

Gradient = (Y2 - Y1)/(X2 - X1)

               = (3 - 0)/(2 - 0)

              = 3/2

Find the gradient of the line that passes through (2, -2) and (6, 4)

Gradient = (Y2 - Y1)/(X2 - X1)

               = (4 + 2) / (6 - 2)

               = 6/4

               = 3/2

Since both the gradient are the same

⇒ The lines are parallel

Answer 2

Given:

Line 1: ( 0, 0 ) ( 2, 3)

Line 2: ( 2, -2 ) ( 6, 4 )

To find:

To prove both the lines are parallel.

Condition:

The gradient of both the lines should be same.

Solution:

For line 1:

(0,0) and (2,3)

Gradient = ( Y2 - Y1 ) / ( X2 - X1 )

Gradient = ( 3 - 0 ) / ( 2 - 0 )

Gradient for line 1 = 3/2

For line 2:

( 2, -2 ) and ( 6, 4 )

Gradient = ( Y2 - Y1 ) / ( X2 - X1 )

Gradient = (4 + 2) / (6 - 2)

Gradient for line 2 = 3/2

Gradient of line 1 and line 2 = 3/2

As the gradient of both the lines are the same, the lines are parallel.

Hence, proved.