Question

Find the coordinates of P which divides the line segment joining A(3, 7) and B(9, 4), such that
5AP = 4PB.​

Answer 1

Answer:

We know that by section formula, the co-ordinates of the points which divide internally the line segment joining the points (x  

1

​  

,y  

1

​  

) and (x  

2

​  

,y  

2

​  

) in the ratio m:n is

(x,y)=(  

m+n

mx  

2

​  

+nx  

1

​  

 

​  

,  

m+n

my  

2

​  

+ny  

1

​  

 

​  

)

The end points of AB are A(4,-3) and B(9,7).

Therefore,

(x  

1

​  

=4,y  

1

​  

=−3) and (x  

2

​  

=9,y  

2

​  

=7)

Also, m=3 and n=2

Let the required point be P(x,y).

Using section formula,  

x=  

m+n

mx  

2

​  

+nx  

1

​  

 

​  

,y=  

m+n

my  

2

​  

+ny  

1

​  

 

​  

 

x=  

5

3×9+2×4

​  

=7,y=  

5

3×7+×−3

​  

=3

Therefore, the required point is P(7,3).

Step-by-step explanation:

Answer 2

Step-by-step explanation:

1. ratio = 4:5
2. coordinates = A(3,7),B(9,4)
3. taking formula = m1×x2+m2×x1/m1+m2
4. x = 9*4+5*3/4+5=51/9 = 17/3 ans
5. y= 5*7+4×4/4+5 = 51/9 =17 / 3 ans