the line segment ab meets the coordinates axis in points a and B if a point p a B in the ratio 2 is to 3 then find the points a and B
Answers
Answer:
The line segment AB meets the coordinates axes in points A and B. If point P(3,6) divides AB in the ratio 2:3,then find the points A and B
Step-by-step explanation:
the co-ordinates of A and B be (x,0)≡(x
1
,y
1
) and (0,y)≡(x
2
,y
2
)
∵ The co-ordinates of a point P(−3,4) on AB divides it in the ratio 2:3.
i.e., AP:PB=2:3
∴ m=2 and n=3
and x=−3 and y=4
By using section formula, we get
−3=
2+3
2×0+3×x
........[∵x=
m
1
+m
2
m
1
x
2
+m
2
x
1
]
−3=
5
3x
⇒3x=−15
⇒x=−5
and 4=
2+3
2×y+3×0
.......[∵y=
m
1
+m
2
m
1
y
2
+m
2
y
1
]
4=
5
2y
⇒2y=20
⇒y=10.
Hence, the co-ordinates of A and B are (−5,0) and (0,10).
Answered By
toppr
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