A line passes through $(9 ,2 )$ and $( 4, 8 )$ . A second line passes through $( 4, 1 )$ . 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 · 2018-01-18T09:00:26

One other point has coordinates $color(purple)(2, 3.4)$

Since the two lines are parallel, their slopes are equal.

Slope of first line is
$m_1 = (y2 - y1) / (x2 - x1) = (8-2) / ( 4-9) = -(6/5)$

Slope of second line $m2 = m1 = -(6/5)$

Equation of second line is

$y - 1 = -(6/5) (x - 4)$

$5y + 6x = 29$

Let x = 2, then

$5y + 12 = 29$

$y = 17/5 = 3.4$

One other point has coordinates $color(purple)(2, 3.4)$

A line passes through (9 ,2 )(9 ,2 ) and ( 4, 8 )( 4, 8 ). A second line passes through ( 4, 1 )( 4, 1 ). What is one other point that the second line may pass through if it is parallel to the first line?