A line passes through #(6 ,4 )# and #(9 ,2 )#. A second line passes through #(3 ,4 )#. 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 · 2018-01-07T15:07:11

One other point is #(1, (16/3))# through which the second line CD will pass through

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Let the coordinates of A (6,4) & B (9,2)

Slope of AB #m = (y_2 - y_1) / (x_2 - x_1) = (2 - 4) / (9 - 6) = -(2/3)#

Slope of AB = Slope of CD as they are parallel.

Equation of CD is

#(y - y_3) = m (x - x_3)# where coordinates of C is (3,4)

#y - 4 = -(2/3) (x - 3)#

#3y - 12 = -2x + 6#

#2x + 3y = 18#

By Substituting different values for x, one can arrive at the corresponding value for y in the above equation.

When x = 1, #y = (18 - 2) / 3 = 16/3#