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?

Question

1851 views around the world

You can reuse this answer
Creative Commons License

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

enter image source here

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