The-point-4-1-undergoes-the-following-two-successive-transformations-i-reflection-about-the-line-y-x-ii-translation-through-a-distance-2-units-along-the-positive-x-axis-then-find-the-final-coord

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Question Number 77001 by vishalbhardwaj last updated on 02/Jan/20

$$\mathrm{The}\mathrm{point}(4,1)\mathrm{undergoes}\mathrm{the}\mathrm{following}$$$$\mathrm{two}\mathrm{successive}\mathrm{transformations}$$$$\left(\mathrm{i}\right)\mathrm{reflection}\mathrm{about}\mathrm{the}\mathrm{line}\mathrm{y}=\mathrm{x}$$$$\left(\mathrm{ii}\right)\mathrm{translation}\mathrm{through}\mathrm{a}\mathrm{distance}$$$$2\mathrm{units}\mathrm{along}\mathrm{the}\mathrm{positive}\mathrm{x}\mathrm{axis}$$$$\mathrm{then}\mathrm{find}\mathrm{the}\mathrm{final}\mathrm{coordinates}$$$$\mathrm{of}\mathrm{the}\mathrm{point}????$$

Answered by MJS last updated on 02/Jan/20

$$\mathrm{reflection}\mathrm{about}y=x\mathrm{just}\mathrm{exchanges}\mathrm{the}$$$$\mathrm{values}\mathrm{of}x\mathrm{and}y$$$$\left(\mathrm{i}\right)\to \left(\begin{array}{c}1\\ 4\end{array}\right)$$$$\left(\mathrm{ii}\right)\to \left(\begin{array}{c}3\\ 4\end{array}\right)$$

Commented by vishalbhardwaj last updated on 03/Jan/20

$$\mathrm{I}\mathrm{did}\mathrm{not}\mathrm{get}\mathrm{it}\mathrm{sir},\mathrm{please}\mathrm{explain}\dots$$

Commented by MJS last updated on 03/Jan/20

$$\mathrm{just}\mathrm{draw}\mathrm{it}.P=\left(\begin{array}{c}x\\ y\end{array}\right)\mathrm{reflected}\mathrm{about}y=x$$$$\Rightarrow P_1=\left(\begin{array}{c}y\\ x\end{array}\right).\mathrm{translation}\mathrm{along}\mathrm{the}\mathrm{positive}$$$$x-\mathrm{axis}=\mathrm{slide}\mathrm{to}\mathrm{the}\mathrm{right}\mathrm{parallel}\mathrm{to}x-\mathrm{axis}$$$$\mathrm{add}d\mathrm{istance}\mathrm{to}x-\mathrm{value}{P}_2=\left(\begin{array}{c}y+d\\ x\end{array}\right)$$

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