The line through A(-2, 3) and B(4, b) is perpendicular to the line 2x - 4y = 5. Find the value of b.

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Solution

The correct option is A $- 9$
$sin c e space t h e space l i n e s space a r e space p e r p e n d i c u l a r h e n c e space t h e space p r o d u c t space o f space s l o p e space o f space b o t h space t h e space l i n e s space i s space minus 1 s o s l o p e space o f space 2 x minus 4 y space equals space 5 4 y space equals space 2 x minus 5 y space equals space 2 over 4 x minus 5 over 4 t h i s space i s space o f space t h e space f o r m space y space equals space m x plus c m subscript 1 space equals space 1 half s l o p e space o f space l i n e space t h r o u g h space A B thin space m subscript 2 space equals space fraction numerator B subscript y minus A subscript y over denominator B subscript x minus A subscript x end fraction m subscript 2 space equals space fraction numerator b minus 3 over denominator 4 minus open parentheses negative 2 close parentheses end fraction space equals space fraction numerator b minus 3 over denominator 6 end fraction m subscript 1. m subscript 2 space equals space 1 half cross times fraction numerator b minus 3 over denominator 6 end fraction space equals space minus 1 h e n c e space fraction numerator b minus 3 over denominator 12 end fraction space equals space minus 1 b minus 3 space equals space minus 12 b space equals space minus 9$

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Similar questions

The line through A(-2, 3) and B(4, b) is perpendicular to the line 2x - 4y = 5. Find the value of b.

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