Question

find the ratio in which the point (k,2) divided the line segment joining the point A (12,5) and B ( 4,-3 ) and also find the value of k
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Answer 1

Explanation:

Let the ratio be m:n

Then,my2+ny1/m+n=m(−3)+n(5)/m+n=2

⇒ −3m+5n=2m+2n

⇒ −5m=−3n

⇒ m/n=3/5

⇒ m:n=3:5

Now,

mk2+nk2/m+n=k

⇒ 3(4)+5(12)/3+5=k

⇒ 8x=12+60

⇒ 8x=72

⇒x= 72/8

x=9