Find the slope of the line perpendicular to AB if :

(i) A = (0, -5) and B = (-2, 4)

(ii) A = (3, -2) and B = (-1, 2)

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Solution

$i right parenthesis s l o p e space o f A B equals fraction numerator 4 plus 5 over denominator negative 2 minus 0 end fraction equals fraction numerator negative 9 over denominator 2 end fraction s l o p e space o f space t h e space l i n e space p e r p e n d i c u l a r space t o space A B equals fraction numerator negative 1 over denominator s l o p e space o f space A B end fraction equals 2 over 9 i i right parenthesis s l o p e space o f A B equals fraction numerator 2 plus 2 over denominator negative 1 minus 3 end fraction equals fraction numerator 4 over denominator negative 4 end fraction equals negative 1 s l o p e space o f space t h e space l i n e space p e r p e n d i c u l a r space t o space A B equals fraction numerator negative 1 over denominator s l o p e space o f space A B end fraction equals 1$

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A (4, 3)

B (6, 4)

A B

P (7, 3)

Q (0, - 4)

Find the slope and the inclination of the line AB if :

(i) A = (-3, -2) and B = (1, 2)

(ii) A = $(0, - \sqrt{3})$ and B = (3, 0)

(iii) A = $(- 1, 2 \sqrt{3})$ and B = $(- 2, \sqrt{3})$

A B

A = (0, - 5)

B = (- 2, 4)

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