Question

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AM BACK WITH BRAIN PAIN QUESTION...

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QUESTION IS IN ATTACHMENT..

Answer 1

Let the cordinates of point D be (x,y)

Now,

Given that

EF is four time of DE,

4DE= EF,

DE + DF = EF

DE + DF = 4DE

DF = 3DE

DE/DE = 1/3

Now, we know that ,

a line, passing through cordinates (x₁,y₁) and (x₂,y₂) if it divided into two part in the ratio of m and n then the cordinates of that point be

(mx₂+nx₁)/(m+n) and (my₂ + ny₁)/(m+n)

Now,According to question,

x₁= 6

y₁=4

x₂=14

y₂=12

m= 1

n=3

Now,

x = (mx₂+nx₁)/(m+n)

x = (1*14 + 3*6)/(1+3)

x= (14 + 18)/4

x= 32/4

x= 8

Again,

y= (my₂ + ny₁)/(m+n)

y=(1*12 +3*4)/(1+3)

y = (12+12)/4

y= 24/4

y= 6

Hence ,

Cordinates of D = (8,6)