Question

(b) Determine the ratio in which y-x+2=0 divides the line joining the points
(3,-1) and (8,9).
[3]​

Answer 1

Answer:

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Answer 2

Answer:

Given that two points are (3,-1)=(x1,y1) and (8,9)=(x2,y2)

Also equation of line which divides = y - x +2 =0

or x - y - 2=0

or x - y = 2......( 1 )

Using 2 point form of Straight Lines

( y - y1 ) = y2 - y1 × ( x - x1 )

x2 - x1

=> ( y + 1 ) = 9 + 1 × ( x - 3 )

8 - 3

=> ( y + 1 ) = 2 × ( x - 3 )

=> 2x - 6 = y + 1

=> 2x - y = 7........( 2 )

SOLVING ( 1 ) & ( 2 )

x = 5 and y = 3

=> Point on which line divides = ( 5,3 )

Let ratio in which the line divides = k : 1

Using section formula on points

k : 1

(3,-1) •—————•—————• (8,9)

(5,3)

x = mx2 + nx1 = 8k + 3 = 5

m + n k + 1

On solving we get

8k + 3 = 5k + 5

3k = 2

k = 2/3

The required ratio is k : 1 = 2/3 : 1 = 2 : 3

Thats kinda Lengthy

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