Write down the coordinate of the point P that divides the line joining A (-4,1) and B
(17,10) in the ratio 1:2. In what ratio does the y axis divide the line AB
Answers
Answer:
(i) Let P(x,y) divides the line segment joining the points A(−4,1),B(17,10) in the ratio 1:2,
Here, X
1
=−4,y
1
=1
x
2
=17,y
2
=10
m:n=1:2
∴ By section formula, x=(mx
2
+nx
1
)/(m+n)
∴x=(1×17+2×−4)/(1+2)
∴x=(17+(−8))/3
∴x=9/3
∴c=3.
By section formula y=(my
2
+ny
1
)/(m+n)
∴y=(1×10+2×1)/(1+2)
∴y=(10+2)/3
y=12/3=4.
Hence the co-ordinates of the point P are (3,4).
(ii) Since O is the origin, the co-ordinates of O are (0,0).
By distance formula, d(OP)=
[(x
2
−x
1
)
2
+(y
2
−y
1
)
2
]
∴d(OP)=
[(0−3)
2
+(0−4)
2
]
∴d(OP)=
[(3)
2
+(4)
2
]
∴d(OP)=
(9+16)
∴d(OP)=
25
=5.
Hence the distance OP is 5 units.
(iii) Let m:n be the ratio in which Y axis divide the line AB.
Since, AB touches Y axis, its x co-ordinate will be zero,
Here x
1
=−4,y
1
=1
x
2
=17,y
2
=10
∴ By section formula, x=(mx
2
+nx
1
)/(m+n)
∴0=(m×17+n×−4)/(m+n)
∴0=(17m−4n)/(m+n)
⇒17m−4n=0
⇒17m=4n
⇒m/n=4/17
∴m:n=4:17
Hence the ration in which Y axis divide line AB is 4:17.
Step-by-step explanation: