The line passing through (-4, -2) and (2, -3) is perpendicular to the line passing through (a, 5) and (2, -1). Find a.

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Solution

The correct option is C
3
As we know the relation between the slopes of 2 perpendicular line is

M1×M2=-1

ie
$fraction numerator y subscript 2 minus y subscript 1 over denominator x subscript 2 minus x subscript 1 end fraction cross times fraction numerator y subscript 4 minus y subscript 3 over denominator x subscript 4 minus x subscript 3 end fraction equals negative 1 fraction numerator negative 2 plus 3 over denominator negative 4 minus 2 end fraction equals negative left parenthesis fraction numerator a minus 2 over denominator 5 plus 1 end fraction$

6=-(a-2)(-6)
a-2=1
a=3

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