A line passes through #(9 ,3 )# and #( 4, 5 )#. A second line passes through #( 7, 8 )#. 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 · 2018-01-12T17:51:55

One other point through which the second parallel line will pass is (2.5, 10.8)

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Let the two lines be AB & CD.

Both the lines will have same slope ‘m’

Slope of #AB = CD = m = (5-3) / (4-9) = -(2/5)#

Equation of CD is

#y = mx + c = -(2/5)x + c#

Substituting the values of x, y of point C, we get the value of constant c

#8 = -((2/5) * 7) + c#

#c = 8+ (2/5) * 7 = 10.8#

Equation of parallel CD is

#y = -(2/5)x + 10.8#

By choosing a value for x in the above equation arbitrarily and substituting the same in this equation, we can get the. Coordinate.

Let x = (5/2), then

#y = (-5/2)(2/5)) + 10.8 = 9.8#

One other point through which the second parallel line will pass is (2.5, 10.8)