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Alex_Xolod [135]
2 years ago
5

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 o

f point D are (8,5).
The equation of line CD is y =
Mathematics
2 answers:
tensa zangetsu [6.8K]2 years ago
8 0

Answer: Lines AB and CD are parallel. Using the given coordinates

The equation of line CD is y= -1/4x + 7

Step-by-step explanation:

adoni [48]2 years ago
5 0

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

<h3>What are parallel lines?</h3>

" 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.

Learn more about parallel lines here

brainly.com/question/16701300

#SPJ2

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