Question

Lines AB and CD are parallel. The coordinates of point A are (-2,5), the coordinates of point B are (6,3), and the coordinates of point D are (8,5).
The equation of line CD is y =

Answer 1

Equation of the line CD is equals to $y = \frac{-x}{4} +7$.

What are parallel lines?

" Parallel lines are defined as the lines in the same plane never intersect with each other. They are equidistant to each other in the same plane."

Formula used

$Slope = \frac{y_{2} -y_{1} }{x_{2}-x_{1} }$

According to the question,

Given,

Coordinates of A $(x_{1},y_{1})$ = ( -2 , 5)

Coordinates of B $(x_{2},y_{2})$ = ( 6 , 3)

Substitute the value to get the slope of line AB we get,

$Slope of line AB 'm_{1}' =\frac{3-5}{6-(-2)}$

                    ⇒ $m_{1} = \frac{-2}{8}$          

                              $= \frac{-1}{4}$

Coordinates of C $(x_{1},y_{1})$ = ( x ,y)

Coordinates of B $(x_{2},y_{2})$ = ( 8,5)

Substitute the value to get the slope of line CD we get,

$Slope of line CD 'm_{2}' =\frac{5-y}{8-x}$

Lines AB and CD are parallel.

Slope of parallel lines are equal.

Therefore,

                     $m_{2} = m_{1}$          

                 ⇒ $\frac{5-y}{8-x}$ $= \frac{-1}{4}$

                ⇒$5-y = \frac{-1}{4} (8-x)$

                ⇒ $y = \frac{-x}{4} +7$

Hence, equation of the line CD is equals to $y = \frac{-x}{4} +7$.

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