The point (4$$, $$1) undergoes the followingthree transformations successively. (i) reflection about the line $$y=x(ii)$$ transformation through a distance $$2$$ units along thepositive direction of $$x-$$ axis (iii) rotation through an angle $$p/4$$ about the origin inthe counter clockwise direction. Then the final positionof the point is given by the coordinates

Question

The point (4$$, $$1)  undergoes the followingthree transformations successively. (i)  reflection about the line $$y=x(ii)$$  transformation through a distance $$2$$ units along thepositive direction of $$x-$$ axis  (iii)   rotation through an angle $$p/4$$ about the origin inthe counter clockwise direction. Then the final positionof the point is given by the coordinates

Infinity Learn · Accepted Answer

Reflection of the point (4$$, $$1) about the line $$y=x$$ is  (1$$,$$4)  which is transfered to the point (3$$,$$4)  at a distance $$2units$$ along the positive direction of $$x-$$ axis Finally a rotation through an angle π$$/4$$ takes it $$to(3cos$$⁡$$($$π$$/4)$$−$$4sin$$⁡$$($$π$$/4))$$,$$(3sin$$⁡$$($$π$$/4)+4cos$$⁡$$($$π$$/4))=$$−$$12$$,$$72$$

Cartesian plane

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Cartesian plane

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Reflection of the point (4, 1) about the line y=x is (1,4) which is transfered to the point (3,4) at a distance 2units along the positive direction of x- axis Finally a rotation through an angle π/4 takes it to(3cos⁡(π/4)−4sin⁡(π/4)),(3sin⁡(π/4)+4cos⁡(π/4))=−12,72

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