A line passes through #(2 ,8 )# and #( 3, 5 )#. A second line passes through #( 6, 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 · 2018-02-05T02:57:57

#color(brown)(D (2, 16))# is one other point on the line CD which is parallel to the other line AB

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Given AB || CD

#A (2,8), B (3,5), C (6,4)#

To find D(x,y)

Slope of AB #m_(AB) = (y_B - y_A) / (x_B - x_A)#

m_(AB) = (5-8) / (3-2) = -3#

Slope of CD is same as slope of AB as both the lines are parallel.

#:. m_(CD) = m_(AB) = -3#

Equation of line passing through C and parallel to AB is

#y - y_C = m_(CD) (x - x_C)#

#y - 4 = -3 * (x - 6)#

#y - 4 = -3x + 18#

Eqn of CD is #y + 3x = 22#

Let x = 2. The y = 22 - 6 = 16#

#color(brown)(D (2, 16))# is one other point on the line CD which is parallelto the other line AB