A line passes through #(8 ,5 )# 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 · 2018-01-18T07:55:37

One other point has coordinates #color(red)(6,5.5)#

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Let the two lines be m,n

Slope of line m #m_m = (4-5) / (2-8) =( -1) / (-6) = 1/6#

Since lines m and n are parallel,

Slope of the lines are equal.

#:. m_m = m_n = (1/6)#

Eqn of line ‘n’ is

#y - 5 = (1/6)(x - 3)#

#6y - x = 27#

By substituting a value of 6 for x in the above equation , we can evaluate the corresponding value of y

#6y - 6 = 27#

#y = 5.5#

One other point has coordinates #color(red)(6,5.5)#