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Home » State whether the following statements are true or false. Justify your answer. The points (0, 5), (0, –9) and (3, 6) are collinear.
State whether the following statements are true or false. Justify your answer. The points (0, 5), (0, –9) and (3, 6) are collinear.
CBSE | Class 10 | Coordinate Geometry | Exercise 7.2 | Maths | NCERT Exemplar
State whether the following statements are true or false. Justify your answer. The points (0, 5), (0, –9) and (3, 6) are collinear.

Solution:

The statement given in the question is false.

Justification:

If the area of a triangle formed by its points equals 0, then the points are collinear.

Provided,

{{x}_{1}}~=\text{ }0,\text{ }{{x}_{2}}~=\text{ }0,\text{ }{{x}_{3}}~=\text{ }3and

{{y}_{1}}~=\text{ }5,\text{ }{{y}_{2}}~=\text{ }\text{ }9,\text{ }{{y}_{3}}~=\text{ }6

Since, 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)+4\left( 5+9 \right) \right]

=\frac{1}{2}\left( 0+0+3\times 14 \right)

=42/2=21\ne 0

It is clear from the above equation, that the points are not collinear.

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