Question

find the value of k for which the following points are collinear
A 5,4
B 7,K
C 9,-2​

Answer 1

Answer:

value of k = 1

Step-by-step explanation:

Given A(5,4),B(7,k) and C(9,-2)

$Slope\: of\: a \:line \: joining \\the \:points \:(x_{1)},y_{1}) \:and\: \:(x_{2)},y_{2}) \:is\:\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$

$slope \:of \: line \: segment \:AB \\=slope \:of \: line \: segment \:BC$

/* Given , points are collinear */

$\frac{k-4}{7-5}=\frac{-2-k}{9-7}$

$\implies \frac{k-4}{2}=\frac{-2-k}{2}$

$\implies k-4=-2-k$

$\implies k+k = -2+4$

$\implies 2k = 2$

$\implies k = 1$

Therefore,

value of k = 1

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Answer 2

Answer:

Step-by-step explanation: