Quadrilaterals $H D K N$ and $H^{\prime} D^{\prime} K^{\prime} N^{\prime}$ are shown on the coordinate grid where quadrilateral $H^{\prime} D^{\prime} K^{\prime} N^{\prime}$ is a transformation of quadrilateral $H D K N$ . $\newline$ Which algebraic description describes the transformation? $\newline$ A $(x, y) \rightarrow(x-5, y-3)$ $\newline$ B $\quad(x, y) \rightarrow(x-2, y-2)$ $\newline$ C $(x, y) \rightarrow(x+2, y+2)$ $\newline$ D $\quad(x, y) \rightarrow(x+5, y+3)$

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Algebra 2

Find the vertex of the transformed function

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Q. Quadrilaterals

H D K N

and

H^{\prime} D^{\prime} K^{\prime} N^{\prime}

are shown on the coordinate grid where quadrilateral

H^{\prime} D^{\prime} K^{\prime} N^{\prime}

is a transformation of quadrilateral

H D K N

\newline

Which algebraic description describes the transformation?

\newline

(x, y) \rightarrow(x-5, y-3)

\newline

\quad(x, y) \rightarrow(x-2, y-2)

\newline

(x, y) \rightarrow(x+2, y+2)

\newline

\quad(x, y) \rightarrow(x+5, y+3)

Compare Coordinates: To determine the transformation, we need to compare the coordinates of corresponding vertices from quadrilateral $HDKN$ to quadrilateral $H'D'K'N'$ .
Calculate Differences: Let's assume we have the coordinates of a vertex $H$ from $HDKN$ and its corresponding vertex $H'$ from $H'D'K'N'$ . We will calculate the difference in the $x$ -coordinates and the $y$ -coordinates.
Describe Transformation: If $H$ has coordinates $(x_H, y_H)$ and $H'$ has coordinates $(x_H', y_H')$ , then the transformation can be described by $(x_H', y_H') = (x_H + \Delta x, y_H + \Delta y)$ , where $\Delta x$ is the change in the $x$ -coordinate and $\Delta y$ is the change in the $y$ -coordinate.
Examine Options: By examining the options given, we can see that each option represents a different transformation: A represents a translation $5$ units left and $3$ units down, B represents a translation $2$ units left and $2$ units down, C represents a translation $2$ units right and $2$ units up, and D represents a translation $5$ units right and $3$ units up.
Need Specific Coordinates: Without the specific coordinates of the vertices, we cannot determine the exact transformation. We need the coordinates to proceed with the calculation.
Cannot Determine Transformation: Since we do not have the specific coordinates, we cannot calculate the differences in the $x$ and $y$ values to match with one of the given options ( $A$ , $B$ , $C$ , or $D$ ). Therefore, we cannot provide a final answer to the question prompt.