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(i) 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. (ii) Calculate the distance OP, where O is the origin. - Mathematics

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Sum

(i) 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.
(ii) Calculate the distance OP, where O is the origin.
(iii) In what ratio does the Y-axis divide the line AB?

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Solution

(i) Co-ordinates of point P are

`((1xx17+2xx(-1))/(1+2),(1xx10+2xx1)/(1+2))`

`=((17-8)/3,(10+2)/3)`

`=(9/3,12/3)`

`=(3,4)`

(ii) `OP=sqrt((0-3)^2+(0-4)^2)`

`OP=sqrt(9+16)`

`OP=sqrt25`

`OP=5` units

(iii) Let AB be divided by the point P(0, y) lying on y-axis in the ratio

`therefore (0,y)=((kxx17+1xx(-4))/(k+1),(kxx10+1xx1)/(k+1))`

`=>(0,y)=((17k-4)/(k+1),(10k+1)/(k+1))`

`=>0=(17k-4)/(k+1)`

`=>17k-4=0`

`=>k=4/17`

Thus, the ratio in which the y-axis divide the line AB is 4: 17.

Concept: Section Formula
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APPEARS IN

Selina Concise Maths Class 10 ICSE
Chapter 13 Section and Mid-Point Formula
Exercise 13 (C) | Q 12 | Page 183

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