Question

find the value of k is coordinate of the points A (2,-2),B (-4,2), C (-7,k) are collinear


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Answer 1

Given :-

• Coordinates of A = ( 2 , - 2 )
• Coordinates of B = ( - 4 , 2 )
• Coordinates of C = ( - 7 , k )

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To Find :-

• Value of k if given points are collinear

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Solution :-

Given points are collinear therefore area of triangle formed by points is 0

$\bigstar\: \boxed{\sf Area = \dfrac{1}{2} \bigg [x_1(y_2 -y_3) +x_2(y_3 -y_1) +x_3( y_1 -y_2) \bigg ]}$

$\longmapsto \sf \dfrac{1}{2} \bigg [2(2 -k) - 4(k + 2) - 7( - 2-2 \bigg ] = 0$

$\longmapsto\sf \dfrac{1}{2} \bigg [4 - 2k - 4k - 8 + 28\bigg ] = 0$

$\longmapsto\sf \dfrac{1}{2} \bigg [- 6k + 24\bigg ] = 0$

$\longmapsto \sf - 3k + 12 = 0$

$\longmapsto\sf - 3k = - 12$

$\longmapsto\sf k = \frac{ - 12}{ - 3}$

$\longmapsto \boxed{\sf k = 4 }$

Answer 2

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