Question

One line passes through the points (-7, 4) and (5, -4). Another line passes through points (-7, -4) and (2, 2). Are the lines parallel, perpendicular, or neither?

Answer 1

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We just need to find the slope of both lines.

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IF their slopes are same they are parallel.

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IF their slopes are negative and inverse with each other , they are perpendicular ,

thus when we multiply them the answer must equals - 1 .

Which means :

slope ( L 1 ) × slope ( L 2 ) = - 1

++++++++++++++++++++++++++++++++++++

And Neither when none of above phrases happened.

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LINE (1)

A = ( - 7 , 4 ) & B = ( 5 , - 4 )

We have following equation to find the slope using two points :

$slope = \frac{y( B) - y( A) }{x( B) - x( A) }$

Now just need to put coordinates in the above equation :

$slope = \frac{ - 4 - 4}{5 - ( - 7)}$

$slope = \frac{ - 8}{5 + 7}$

$slope = - \frac{8}{12}$

$slope = - \frac{2}{ 3}$

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LINE (2)

C = ( - 7 , - 4 ) & D = ( 2 , 2 )

$slope = \frac{y( D) - y( C) }{x( D) - x( C) }$

Put the coordinates.

$slope = \frac{2 - ( - 4)}{2 - ( - 7)}$

$slope = \frac{2 + 4}{2 + 7}$

$slope = \frac{6}{9}$

$slope = \frac{2}{3}$

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CHECK ;

$- \frac{2}{3} ≠\frac{2}{3}$

Thus they are not parallel .

$- \frac{2}{ 3} \times \frac{2}{3} = - \frac{4}{9} ≠ - 1$

Thus they are not perpendicular.

So Neither.

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Done...

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