A line passes through #(4 ,3 )# and #(1 ,4 )#. A second line passes through #(7 ,8 )#. What is one other point that the second line may pass through if it is parallel to the first line?

1 Answer
P dilip_k
Jul 15, 2016

Let the coordinate of other point be #(h,k)#

The slope of the 1st line passing through #(4,3) and (1,4)# is #=(3-4)/(4-1)=-1/3#

The slope of the 2nd line passing through #(h,k) and (7,8)# is #=(k-8)/(h-7)#

By the given condition of the problem the 2nd line is parallel
to the !st one . So their slope will be equal.

#=>(k-8)/(h-7)=-1/3#

#=>h-7=3k-24#

#=>h-3k+17=0#

Replacing #h->x and k->y# we get an equation of a straight line

#x-3y+17=0 ----(1)#
#color(blue)(-> "Any point on this straight line may be our other point")#.

Plugging in 20 for x in equation (1) we get y = 1, so #(color(red)(1,20))# may be the coordinate of other point among infinite number of possibilities.

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