If a line joining two points A $$($$ $$2$$, $$0)$$ and B $$($$ $$3$$, $$1)$$ is rotated about A in anticlockwise direction through an angle $$15$$° such that the point B goes to C in the new position, then the coordinates of C are

Question

If a line joining two points A $$($$ $$2$$, $$0)$$ and B $$($$ $$3$$, $$1)$$ is rotated about A in anticlockwise direction through an angle $$15$$° such that the point B goes to C in the new position, then the coordinates of C are

Infinity Learn · Accepted Answer

The equation of AC isx−$$2cos$$⁡$$60$$∘$$=y$$−$$0sin$$⁡$$60$$∘$$=rWe$$ have, $$AB=(3$$−$$2)2+(1$$−$$0)2=2As$$ ACis the new position of AB. Therefore, $$AC=AB=2$$.Thus, the coordinates of C are given by   x−$$2cos$$⁡$$60$$∘$$=y$$−$$0sin$$⁡$$60$$∘$$=2$$⇒$$x=2+12$$,$$y=32Hence$$, the coordinates of C are $$2+12$$,$$32$$.

If a line joining two points $A (2, 0)$ and $B (3, 1)$ is rotated about $A$ in anticlockwise direction through an angle $15 °$ such that the point $B$ goes to $C$ in the new position, then the coordinates of $C$ are

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If a line joining two points A ( 2, 0) and B ( 3, 1) is rotated about A in anticlockwise direction through an angle 15° such that the point B goes to C in the new position, then the coordinates of C are

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Ready to Test Your Skills?

free study material

If a line joining two points $A (2, 0)$ and $B (3, 1)$ is rotated about $A$ in anticlockwise direction through an angle $15 °$ such that the point $B$ goes to $C$ in the new position, then the coordinates of $C$ are