The slope of GH is 5. Which segments are parallel to GH ?Choose all answers that are correct. PQ, where P is at (4, 15) and Q is at (2, 5)RS, where R is at (3, 6) and S is at (8, 7)TU, where T is at (6, 4) and U is at (11, 3)WX, where W is at (3, 1) and X is at (4, 6)

The correct answers are:
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  [A]:  " PQ, where P is at (4, 15) and Q is at (2, 5) " ;  AND:
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  [D]:  " WX, where W is at (3, 1) and X is at (4, 6) " .
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Explanation:
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Note:  if the slope is the same (i.e., if the "slope" is "5" ), then the segment is "parallel" .

  The slope, "m" :   m = (y₂ - y₁) / (x₂ - x₁) ;
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Consider the answer choices:
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 [A]:  "(4, 15)" and "(2, 5)" .  y₂ = 5 ;  y₁ = 15 ; x₂ = 2 ; x₁ = 4 ; 

       m =  (y₂ - y₁) / (x₂ - x₁) = (5 - 15) / (2 - 4) = -10/ -2 = 5 .

So choice [A]:  is an answer.
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 [B]:  "(3, 6)" and "(8, 7)" .  y₂ = 7 ;  y₁ = 6 ; x₂ = 8 ;  x₁ = 3 ; 

       m =  (y₂ - y₁) / (x₂ - x₁) = (7 - 6) / (8 - 3) = 1 /5 ;   1/5 [tex] \neq [/tex] 5 ; 

So choice [B]: is NOT an answer.
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 [C]:  "(6, 4)" and "(11, 3)" .  y₂ = 3 ;  y₁ = 4 ; x₂ = 11 ; x₁ = 6 ; 

       m =  (y₂ - y₁) / (x₂ - x₁) = (3 - 4) / (11 - 6) =  -1 /5 ;   1/5 [tex] \neq [/tex] 5 ; 

So choice [C]: is NOT an answer.
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 [D]:  "(3, 1)" and "(4, 6)" .  y₂ = 6 ;  y₁ = 1 ; x₂ = 4 ;  x₁ = 3 ; 

       m =  (y₂ - y₁) / (x₂ - x₁) = (6 - 1) / (4 - 3) =  5 / 1 =  5 ;  ;  
1/5 [tex] \neq [/tex] 5 ; 

So choice [D]:  is an answer.
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The correct answers are:
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  [A]:  " PQ, where P is at (4, 15) and Q is at (2, 5) " ;  AND:
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  [D]:  " WX, where W is at (3, 1) and X is at (4, 6) " .
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