Question

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)

Answer 1

Find the slope of each line, and the line with the same slope as GH will be the answer.

PQ = (5-15)/(2-4) = -10/-2 = 5

RS = (7-6)/(8-3) = 1/5

TU = (3-4)/(11-6) = -1/5

WX = (6-1)/(4-3) = 5/1 = 5

The answers are WX and PQ.

Hope this helps :)

Answer 2

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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Step-by-step 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
`\\eq` 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
`\\eq` 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
`\\eq` 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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