A line passes through #(5 ,6 )# and #(7 ,8 )#. A second line passes through #(2 ,1 )#. What is one other point that the second line may pass through if it is parallel to the first line?

1 Answer
Ratnesh Bhosale
Nov 2, 2016

Infinite points.

Explanation:

#m_1= (y_2-y_1)/(x_2-x_1)#

#m_1= (8-6)/(7-5)#

#m_1=1#

The other line is parallel to first one .So, #m_2=1#

The equation of second line is
#y-y_1= m(x-x_1)#

#y-1= 1(x-2)#

#y-1= x-2#

#x-y=1#-------------(1)

Let the coordinate of the point be #(p,q) #. They will satisfy the above equation. We can't say a specific point to become a line parallel. As a line is set of infinite point.
To state the coordinate of the point there would be one other condition also.
But we can say that the coordinates will satisfy the equation no. 1.

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