A line passes through #(4 ,7 )# and #(2 ,4 )#. A second line passes through #(3 ,5 )#. What is one other point that the second line may pass through if it is parallel to the first line?

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Answer 1 · 2018-02-12T11:24:56

#(5,8)# may be one point through which second line can pass.

The slope of the line passing through #(4,7) and (2,4)# is

#m= (y_2-y_1)/(x_2-x_1)= (4-7)/(2-4)=3/2#

Equation of second line passing through #(3,5)# is

#y-y_1=m(x-x_1) :. y-5=m(x-3)#. Parallel lines have

equal slope. #:.m=3/2# . So equation of second line is

#y-5=3/2(x-3)# If # x=5 ; y-5 =3/2(5-3) or y-5 =3# or

#y=8 :.x=5; y=8 :. (5,8)# may be one point through which

second line may pass. [Ans]