A line passes through $(2, 4)$ $(2 ,4 )$ and $(7, 5)$ $(7 ,5 )$ . 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 · 2017-11-22T12:25:21

$(1, \frac{22}{5})$ $(1 , 22/5 )$

If two lines are parallel, then they have the same gradient. Gradient of the first line:

$\frac{5 - 4}{7 - 2} = \frac{1}{5}$ $(5-4)/(7-2)=1/5$

Equation of second line:

$y - 5 = \frac{1}{5} (x - 3) \Rightarrow y = \frac{1}{5} x + \frac{22}{5}$ $y-5=1/5(x-3)=>y=1/5x+22/5$

The second line will pass through any points of $y = \frac{1}{5} x + \frac{22}{5}$ $y=1/5x+22/5$

Let $x = 1$ $x=1$

$y = \frac{1}{5} (1) + \frac{22}{5} = \frac{23}{5}$ $y=1/5(1)+22/5=23/5$

Coordinates of second point:

$(1, \frac{22}{5})$ $(1 , 22/5 )$

A line passes through (2,4)(2 ,4 ) and (7,5)(7 ,5 ). 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?