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

A line passes through (2 ,8 )(2 ,8 ) and ( 3, 5 )( 3, 5 ). A second line passes through ( 6, 4 )( 6, 4 ). What is one other point that the second line may pass through if it is parallel to the first line?