The point A (2$$, $$l) is translated parallel to the line x $$-$$ y $$=$$ $$3$$ by a distance of $$4$$ units. If the new position $$A1$$ is in the third quadrant, then the coordinates of $$A1$$ are

Question

The point  A (2$$, $$l) is translated parallel to the line x $$-$$ y $$=$$ $$3$$ by a distance of $$4$$ units. If the new position $$A1$$ is in the third quadrant, then the coordinates of $$A1$$ are

Infinity Learn · Accepted Answer

Since the point $$A(2$$, $$1)$$ is translated parallel to x $$-$$ y $$=$$ $$3$$, AA' has the same slope as that of x $$-$$ y $$=$$ $$3$$. Therefore, AA' passes through (2$$, $$1)  and has slope $$1$$. Here, $$tan$$⁡θ$$=1$$ or $$cos$$⁡θ$$=1/2$$,$$sin$$⁡θ$$=1/2Thus$$, the equation of AA' is x−$$2cos$$⁡$$($$π$$/4)=y$$−$$1sin$$⁡$$($$π$$/4)Since$$ AA' $$=$$ $$4$$, the coordinates of A' are given by x−$$2cos$$⁡$$($$π$$/4)=y$$−$$1sin$$⁡$$($$π$$/4)=$$−$$4$$ or $$x=2$$−$$4cos$$⁡π$$4$$,$$y=1$$−$$4sin$$⁡π$$4$$ or  $$x=2$$−$$22$$,$$y=1$$−$$22$$ Hence, the coordinates of A′ are (2$$−$$22$$,$$1$$−$$22) .

The point A (2, l) is translated parallel to the line x - y = 3 by a distance of 4 units. If the new position A¹ is in the third quadrant, then the coordinates of A¹are

Remember concepts with our Masterclasses.

Ready to Test Your Skills?

free study material

The point A (2, l) is translated parallel to the line x - y = 3 by a distance of 4 units. If the new position A1 is in the third quadrant, then the coordinates of A1 are

Remember concepts with our Masterclasses.

Ready to Test Your Skills?

free study material

The point A (2, l) is translated parallel to the line x - y = 3 by a distance of 4 units. If the new position A¹ is in the third quadrant, then the coordinates of A¹are