A line passes through (4 ,3 )(4,3) and (1 ,4 )(1,4). A second line passes through (7 ,8 )(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)(h,k)

The slope of the 1st line passing through (4,3) and (1,4)(4,3)and(1,4) is =(3-4)/(4-1)=-1/3=3−44−1=−13

The slope of the 2nd line passing through (h,k) and (7,8)(h,k)and(7,8) is =(k-8)/(h-7)=k−8h−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⇒k−8h−7=−13

=>h-7=3k-24⇒h−7=3k−24

=>h-3k+17=0⇒h−3k+17=0

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

x-3y+17=0 ----(1)x−3y+17=0−−−−(1)
color(blue)(-> "Any point on this straight line may be our other point")→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))(1,20) may be the coordinate of other point among infinite number of possibilities.

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