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(C) The initial position of the insect is $A(3, 2)$.Moving $4 \ units$ towards the west (negative $x$-direction) changes the $x$-coordinate: $3 - 4 =

Vedclass · Accepted Answer

$\left( \sqrt{2}, \frac{-3\pi}{4} \right)$

Vedclass · Answer

(C) The initial position of the insect is $A(3, 2)$.Moving $4 \ units$ towards the west (negative $x$-direction) changes the $x$-coordinate: $3 - 4 = -1$. The position becomes $(-1, 2)$.Moving $3 \ units$ towards the south (negative $y$-direction) changes the $y$-coordinate: $2 - 3 = -1$. The final position $B$ is $(-1, -1)$.To find the polar coordinates $(r, 	heta)$ for $B(-1, -1)$:$r = \sqrt{(-1)^2 + (-1)^2} = \sqrt{1 + 1} = \sqrt{2}$.Since the point $(-1, -1)$ lies in the third quadrant,the angle $	heta$ is given by $	heta = -\pi + 	an^{-1}\left(\frac{-1}{-1}ight) = -\pi + \frac{\pi}{4} = -\frac{3\pi}{4}$.Thus,the polar coordinates are $\left( \sqrt{2}, -\frac{3\pi}{4} ight)$.

An insect is resting on the graph paper at a point $A(3, 2)$. Now it starts moving towards the west direction and covers a distance of $4 \ units$,then it turns towards the south and covers a distance of $3 \ units$ to reach point $B$. The polar coordinates of point $B$ will be:

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