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# The vertices of a triangle are A(2, 5), B(1, 2), and C(3, 1). Find the coordinates of the image after the transformations given. Reflect in the x-axis, and then rotate $90^{\circ}$ counterclockwise about the origin.

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We know that when a point is reflected about $\textbf{x-axis}$ then is y-coordinate becomes opposite.

$A(x,\ y)\ \ \rightarrow\ \ A'(x,\ -y)$

$\textbf{Given : }A(2,\ 5),\ \ B(1,\ 2),\ \ C(3, 1)$

\begin{align*} &\textbf{\color{#4257b2}Reflection about the x-axis : }\\ &A(2,\ 5)\ \ \rightarrow\ \ A'(2,\ -5)\\ \\ &B(1,\ 2)\ \ \rightarrow\ \ B'(1,\ -2)\\ \\ &C(3,\ 1)\ \ \rightarrow\ \ C'(3,\ -1) \end{align*}

$\textbf{Coordinate of the image are : A'(2, -5), B'(1, -2), and C'(3, -1)}$

$\textbf{\color{#4257b2}Now rotating above image 90\text{\textdegree} counterclockwise.}$

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