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)#