For what value of x are the points A(−3,12), B(7,6) and C(x,9) collinear?
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Answer:
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.
Step-by-step explanation:
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