Question

For what value of x are the points A( -3 , 12 ) , B ( 7, 6 ) and C ( x , 9 ) are collinear ?

with explanation

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Answer 1

Answer:

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Points are A(−3,12),B(7,6) and C(x,9) are collinear.

Which means area of triangle ABC=0

Hence

Points collinear are:

$\frac{1}{2}(6x - 12) = 0 \\ \\ or \\ \\ x = 2$

Hope it helps you from my side

Answer 2

Answer:

Solution

Points are A(−3,12),B(7,6) and C(x,9) are collinear.

Which means area of triangle ABC=0

Area of a triangle =

2

1

[x

1

(y

2

−y

3

)+x

2

(y

3

−y

1

)+x

3

(y

1

−y

2

)]

=

2

1

[−3(6−9)+7(9−12)+x(12−6)]

=

2

1

[−3×(−3)+7×(−3)+x×6]

=

2

1

[9−21+6x]

=

2

1

[6x−12]

Since points are collinear:

2

1

(6x−12)=0

or x=2.