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  • The points (0, 5), (0, –9) and (3, 6) are collinear.

The points (0, 5), (0, –9) and (3, 6) are collinear.

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Answer.      [False]
The given points area (0, 5), (0, –9) and (3, 6)
If the point area collinear then the area of triangle is 0.
x1 =0    x2 =0     x3 =3
y1=5     y2=9     y3=6
We\, know \, that\, area \, of \, triangle = \frac{1}{2}\left [ x_{1} \left ( y_{2} -y_{3}\right )+x_{2} \left ( y_{3} -y_{1}\right )+x_{3} \left ( y_{1} -y_{2}\right )\right ]
= \frac{1}{2}\left [ 0\left ( -9-6 \right ) +0\left ( 6-5 \right )+3\left ( 5+9 \right )\right ]
= \frac{1}{2}\left [ 0+0+42 \right ]
 = \frac{42}{2}=21 
Area of triangle = 21
Here the area of the triangle is not equal to zero.
Hence, the point is not collinear.

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infoexpert27

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