Question

the point p divides the join A(-5,1) and b(3,5) in the ratio k :1 find the value of k given that the co ordinate of q and r are (1,5)and (7,2)and the area of triangle pqr is 3 sq unit

Answer 1

P (-5, 1) ==========A =======Q(3,5)

use section formula,

point A ={(3K-5)/(1+K) , (5K+1)/(K+1)}

now, A , B, and C points form ∆

use area of ∆ formula ,

ar∆ =1/2|(3K-5)/(K+1)(5+2) +1{-2-(5K+1)/(K+1)} +7{(5K+1)/(K+1)) -5}

±4 =[ (3K-5)(7)/(1+K) +(-2K-2-5K-1)/(1+K) +7(5K+1-5K-5)/(1+K)]

±4(1+K) ={21K -35 -7K -3 -28 }

±4(1 +K) =14K -66

now,

4( 1 + K) = 14K -66

4 + 4K = 14K -66

70 =10 K

K =7

again,

-4( 1+ K ) = 14K -66

-4 -4K = 14 K -66

62 = 18K

K = 31/9

hence ,

K = 7 , 31/9