Question

the line segment ab meets the coordinate axes in points a and b if point p(3,6) divides ab in the ratio 2:3 then find points a and b​

Answer 1

Answer:

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

)

Let 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=\displaystyle\frac{2\times 0+3\times x}{2+3}

−3=53x

⇒3x=−15

⇒x=−5

and 4=

2+3

2×y+3×0

4=

5

2y

⇒2y=20

⇒y=10.

Hence, the co-ordinates of A and B are (−5,0) and (0,10).