A line passes through $(4, 7)$ $(4 ,7 )$ and $(2, 4)$ $(2 ,4 )$ . A second line passes through $(3, 5)$ $(3 ,5 )$ . 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

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

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

$m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}} = \frac{4 - 7}{2 - 4} = \frac{3}{2}$ $m= (y_2-y_1)/(x_2-x_1)= (4-7)/(2-4)=3/2$

Equation of second line passing through $(3, 5)$ $(3,5)$ 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]

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