2. Point that divides the line joining A(-4, 1) and B(17, 10) in the ratio 1 : 2
1. Write down the co-ordinates of the point P that divides the line joining `A(-4,1)` and `B(17,10)` in the ratio `1:2`
Solution:
Let `P(x,y)` divides the line segment joining the points AB in the ratio `1:2`.
The given points are `A(-4,1),B(17,10)`
`:. x_1=-4,y_1=1,x_2=17,y_2=10`
and `m:n=1:2`
By section formula
`x=(mx_2+nx_1)/(m+n)`
`=(1*17+2*-4)/(1+2)`
`=(17-8)/(3)`
`=(9)/(3)`
`=3`
`y=(my_2+ny_1)/(m+n)`
`=(1*10+2*1)/(1+2)`
`=(10+2)/(3)`
`=(12)/(3)`
`=4`
Hence, the co-ordinates of the point `P` are `(3,4)`
2. Write down the co-ordinates of the point P that divides the line joining `A(5,12)` and `B(2,9)` in the ratio `2:1`
Solution:
Let `P(x,y)` divides the line segment joining the points AB in the ratio `2:1`.
The given points are `A(5,12),B(2,9)`
`:. x_1=5,y_1=12,x_2=2,y_2=9`
and `m:n=2:1`
By section formula
`x=(mx_2+nx_1)/(m+n)`
`=(2*2+1*5)/(2+1)`
`=(4+5)/(3)`
`=(9)/(3)`
`=3`
`y=(my_2+ny_1)/(m+n)`
`=(2*9+1*12)/(2+1)`
`=(18+12)/(3)`
`=(30)/(3)`
`=10`
Hence, the co-ordinates of the point `P` are `(3,10)`
3. Write down the co-ordinates of the point P that divides the line joining `A(2,8)` and `B(6,14)` in the ratio `5:3` Externally
Solution:
Let `P(x,y)` divides the line segment joining the points AB in the ratio `5:3`.
The given points are `A(2,8),B(6,14)`
`:. x_1=2,y_1=8,x_2=6,y_2=14`
and `m:n=5:3`
By section formula
`x=(mx_2-nx_1)/(m-n)`
`=(5*6-3*2)/(5-3)`
`=(30-6)/(2)`
`=(24)/(2)`
`=12`
`y=(my_2-ny_1)/(m-n)`
`=(5*14-3*8)/(5-3)`
`=(70-24)/(2)`
`=(46)/(2)`
`=23`
Hence, the co-ordinates of the point `P` are `(12,23)`
4. Write down the co-ordinates of the point P that divides the line joining `A(1,-3)` and `B(3,5)` in the ratio `5:3` Externally
Solution:
Let `P(x,y)` divides the line segment joining the points AB in the ratio `5:3`.
The given points are `A(1,-3),B(3,5)`
`:. x_1=1,y_1=-3,x_2=3,y_2=5`
and `m:n=5:3`
By section formula
`x=(mx_2-nx_1)/(m-n)`
`=(5*3-3*1)/(5-3)`
`=(15-3)/(2)`
`=(12)/(2)`
`=6`
`y=(my_2-ny_1)/(m-n)`
`=(5*5-3*-3)/(5-3)`
`=(25+9)/(2)`
`=(34)/(2)`
`=17`
Hence, the co-ordinates of the point `P` are `(6,17)`
This material is intended as a summary. Use your textbook for detail explanation.
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