Question

A (1,1) and b(2,-3) are two points and d is a point on ab produced such that ad =3ab. Find the coordinates of d

Answer 1

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Answer 2

Given :

Co-ordinates of A :

= ( 1,1)

Co -ordinates of B :

= (2,-3)

D is a point on AB dividing it externally such that :

ad = 3ab

To Find :

Co-ordinates of D = ?

Solution :

∴It is a case of external division and the given ratio ;

AD:AB= 3:1  ( say m:n )

Now the X co-ordinate of D will be :

$= \frac{m(x - coordinate B )-n(x- coordinate A)}{m-n}\int\limits^a_b {x} \, dx$

$=\frac{2m - n}{3-1}$

$=\frac{6-1}{2}$

$=\frac{5}{2}$

And the y coordinate of D will be :

$=\frac{m(ycoordinate B)-n(y coordinate A)}{m-n}$

$=\frac{-9 - 1}{2\\}$

$=-5$

So co-ordinates of D are $(\frac{5}{2}, -5)$