Question

The coordinates of the three vertices of the triangle are A (x1, y1), B (x2, y2), C (x3, y3).

Point D divides AB into internal division ratio I:k, E point divides DC internal division ratio m : k+1, find the coordinates of point E.

Really don't know how to solve this, hope someone can help, thank you very much.​

Answer 1

Explanation:

Using the section formula, if a point (x,y) divides the line joining the points (x

1

​

,y

1

​

) and (x

2

​

,y

2

​

) in the ratio m:n, then

(x,y)=(

m+n

mx

2

​

+nx

1

​

​

,

m+n

my

2

​

+ny

1

​

​

)

The vertices of the triangle are given to be (x

1

​

,y

1

​

),(x

2

​

,y

2

​

) and (x

3

​

,y

3

​

). Let these vertices be A,B and C respectively.

Then the coordinates of the point P that divides AB in l:k will be

(

l+k

lx

2

​

+kx

1

​

​

,

l+k

ly

2

​

+ky

1

​

​

)

The coordinates of point which divides PC in m:k+l will be

⎩

⎪

⎪

⎪

⎨

⎪

⎪

⎪

⎧

​

m+k+l

mx

3

​

+(k+l)

(l+k)

lx

2

​

+kx

1

​

​

​

,

m+k+l

my

3

​

+(k+l)

(l+k)

ly

2

​

+ky

1

​

​

​

⎭

⎪

⎪

⎪

⎬

⎪

⎪

⎪

⎫

​

⇒(

m+k+l

kx

1

​

+lx

2

​

+mx

3

​

​

,

m+k+l

ky

1

​

+ly

2

​

+my

3

​

​

)