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.

Step-by-step 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

)

b

step-by-step explanation:

the word superfluous means unnecessary

step-by-step explanation:

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