Question

find the ratio in which the line line 2 X + 3 Y equal to 10 divide line segment joining the points 1, 2 and 2, 3​

Answer 1

get the answer first you have to find the point of intersection of the given line and the line segment joining the given two points.

The line segment joining the two given points would be:

(y+1)={9-(-1)}/{8-3}*(x-3)

=>y+1=2*(x-3)

=>2x-y-7=0--------------(1) is the equation of the line segment.

Now we have to find the point of intersection of (1) and x-y-2=0 which is (5,3)

Let us say this point divides the line segment in the ratio of k1:k2

then 

5={k1*8+k2*3}/k1+k2

=>3k1-2k2=0

=>k1/k2=2/3

so the ratio is 2:3.

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