Question

If the point c(k,4 )divides the join of points A(2,6) andB(5,1) in the ratio 2:3 ,find the value of k

Answer 1

By section formula
C=(16/5 ,4)
so,
k=16/5

Answer 2

Answer:

$Value \: of \: k = \frac{16}{5}$

Step-by-step explanation:

Let C(k,4) divides the join of points A(2,6) and B(5,1) in the ratio 2:3

/* By section formula :

$If \: the \: Coordinates\:of \:the \:point\:C(x,y)\\ which \: divides \:the\:line \: segment \: joining\\the \: points \: A(x_{1},y_{1})\:and \: B(x_{2},y_{2}),\\internally \:in \: the \: ratio \:m:n\: are$

$</p><p>\left(\frac{mx_{2}+nx_{1}}{m+n}, \frac{my_{2}+ny_{1}}{m+n}\right)$

Here,

$C(k,4) \:divides \: the \: join \: of \: points \\</p><p>A(x_{1},y_{1}) = (2,6) \:and \: B(x_{2},y_{2})=(5,1)$

$\implies k = \frac{mx_{2}+nx_{1}}{m+n}$

$\implies k = \frac{2\times 5+3\times 2}{2+3}$

$\implies k = \frac{10+6}{5}$

$\implies k = \frac{16}{5}$

Therefore,

$Value \: of \: k = \frac{16}{5}$

•••♪