According to the question, point P (a, b) and the image of P (a, b) after reflected in the x-axis be (a, -b)
But it is According to the question as
![\[(-2,c)\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-45216d89060d8bb0c721e314635b970e_l3.png "Rendered by QuickLaTeX.com")
Thus,
![\[a\text{ }=\text{ }-2,\text{ }c\text{ }=\text{ }-b~\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-d9a8b2762e96c84de376e58814820a47_l3.png "Rendered by QuickLaTeX.com")
Next,
If P is reflected in the origin, then its co-ordinates will be (-a, -b)
But it is According to the question as
![\[\left( d,\text{ }5 \right)\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-56384b8469cd69bd7a826b43134ed49b_l3.png "Rendered by QuickLaTeX.com")
Thus,
![\[\begin{array}{*{35}{l}} -b\text{ }=\text{ }5\Rightarrow b\text{ }=\text{ }-5,~ \\ d\text{ }=\text{ }-a\text{ }=\text{ }-\left( -2 \right)\text{ }=\text{ }2, \\ c\text{ }=\text{ }-b\text{ }=\text{ }-\left( -5 \right)\text{ }=\text{ }5~ \\ \end{array}\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-7e9952f57ccdc55f1f4af5d61bc2aea3_l3.png "Rendered by QuickLaTeX.com")
Thus,
![\[a\text{ }=\text{ }-2,\text{ }b\text{ }=\text{ }-5,\text{ }c\text{ }=\text{ }5\text{ }and\text{ }d\text{ }=\text{ }2\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-8da1f4fc14a45d272d77c5d276630857_l3.png "Rendered by QuickLaTeX.com")