M is the mid-point of the line segment joining the points A(0, 4) and B(6, 0). M also divides the line segment OP in the ratio 1 : 3.Find:
(i) co-ordinates of M
(ii) co-ordinates of P
(iii) length of BP

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Solution

(i) M is midpoint of AB
hence
$fraction numerator 0 plus 6 over denominator 2 end fraction comma space fraction numerator 4 plus 0 over denominator 2 end fraction space equals space left curly bracket 3 comma space 2 right curly bracket$

$left parenthesis i i right parenthesis space l e t space t h e space c o o r d i n a t e s space o f space P space i s space left parenthesis a comma space b right parenthesis M space equals space open curly brackets 3 comma space 2 close curly brackets O space equals space open curly brackets 0 comma space 0 close curly brackets s o space b y space s e c t i o n space f o r m u l a e open parentheses fraction numerator 3 space cross times 0 space plus 1 cross times a over denominator 3 plus 1 end fraction comma space fraction numerator 3 cross times 0 space plus space 1 cross times b over denominator 3 plus 1 end fraction close parentheses identical to open parentheses 3 comma space 2 close parentheses s o space a divided by 4 space equals space 3 space s o space a space equals space 12 a n d space b divided by 4 space equals space 2 s o space b space equals space 8$

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