Question

Find the ratio in which the point P (-6, a) divides the join of A (-3,-1) and B(-8,9). Also, find the value of a.

Answer 1

Heya !!!


Let P(-6, A) Divide AB in ratio K:1.



K:1


Here,



M1 = K and M2 = 1




And,


A ( -3 , -1) and B ( -8 , 9)



Here,



X1 = -3 , Y1 = -1 and X2 = -8 , Y2 = 9



Then , By sectional formula , the coordinates of P are :


P ( M1X2/ M1 + M2 , M1Y2+ M2 Y1 / M1+M2)




P( K × (-8) / K +1 , K × (9) / K +1)



P ( -8K/K+1 , 9K / K+1)


But the coordinates of point P is P(-6,A)



Therefore,



-8K/K+1 = -6 and 9K/K+1 = A




Now,



-8K/K+1 = -6



-6( K+1) = -8K




-6K -6 = -8K




-8K + 6K = -6



-2K = -6



K = -6/-2 = 3/1



Hence,


Required ratio is 3:1.




Putting K = 3 in ,


9K / K +1 = A



9 × 3 / 3 +1 = A



27/4 = A






HOPE IT WILL HELP YOU...... :-)

Answer 2

Answer:

I hope it will be helpful for you.

Thank you for your question.