Question

Assertion :Area of the triangle formed by the points $(2,\frac{\pi }{6})$, $(-4,\frac{\pi }{6})$ and $(7,\frac{-11\pi }{6})$ is zero. Reason: Area of the triangle formed by three collinear points is zero.
The correct answer is

• A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
• B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
• C. Assertion is correct but Reason is incorrect
• D. Assertion is incorrect but Reason is correct

Answer 1

The correct option is A Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

We know that if the points are collinear then area of triangle is 0.
Given points are $(2,\frac{\pi }{6})$, $(-4,\frac{\pi }{6})$ and $(7,\frac{-11\pi }{6})$
Area of triangle $△=\frac{1}{2}|r_1{r}_2\sin ({\theta }_2-{\theta }_1)+r_2{r}_3\sin ({\theta }_3-{\theta }_2)+r_3{r}_1\sin ({\theta }_1-{\theta }_3)|$
$=\frac{1}{2}|0-28\sin 2\pi +14\sin 2\pi |$
$△=0$
Hence, the points are collinear.