Question

if points (5,5),(10,k),and (-5,1) are in collinear.then the value of k​

Answer 1

hey mate the answer is 7

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Answer 2

Answer:

Concept:

When the point are collinear so ∆ABC= 0

Find:

We find the value of k

Given:

if points (5,5),(10,k),and (-5,1) are in collinear

Step by step:

Let

$a = (5,5) = ( x_{1} , y_{1})$

$b = (10,k) = ( x_{2} , y_{2})$

$c = ( - 5,1) = ( x_{3} , y_{3})$

Given points (5,5),(10,k),and (-5,1) are in collinear

∆abc=0

$\frac{1}{2} ( x_{1}( y_{2} -y_{3} ) + x_{2}( y_{3} -y_{1} ) + x_{3}( y_{1} -y_{2} ) = 0$

$\frac{1}{2} ( 5( k - 1) + 10( 1 - 5 ) +( - 5)( 5 -k ) = 0$

$\frac{1}{2} (5k - 5 - 40 - 25 + 5k) = 0$

$\frac{1}{2} (10k - 70) = 0$

$10k - 70 = 0$

$10k = 70$

$k = 7$

Hence the value of k is 7