Problem

For \#2-3, draw the image of the figure under the given rotation. 2. $\triangle P Q R ; 90^{\circ}$ about the origin. When no direction is specified, you can assume the rotation is counterclockwise Transformation Rule: $(x, y) \rightarrow-y, x$ \begin{tabular}{|l|l|} \hline $\begin{array}{r}\text { Preimage Coordinates } \\ (x, y)\end{array}$ & Image \\ \hline$P^{\prime}(-2,1)$ & \\ \hline$Q^{\prime}(4,1)$ & \\ \hline$R^{\prime}(4,-3)$ & \\ \hline \end{tabular}

Solution

Step 1 :Given the triangle with vertices at points P(-2, 1), Q(4, 1), and R(4, -3), we are asked to find the image of the triangle under a 90 degree rotation about the origin.

Step 2 :The transformation rule for a 90 degree rotation about the origin is \((x, y) \rightarrow (-y, x)\). This means that we replace each x-coordinate with the negative of the y-coordinate and each y-coordinate with the x-coordinate.

Step 3 :Applying the transformation rule to point P(-2, 1), we get P'(-1, -2).

Step 4 :Applying the transformation rule to point Q(4, 1), we get Q'(-1, 4).

Step 5 :Applying the transformation rule to point R(4, -3), we get R'(3, 4).

Step 6 :The image of the triangle under a 90 degree rotation about the origin is given by the points P'(-1, -2), Q'(-1, 4), and R'(3, 4).

Step 7 :Final Answer: \(\boxed{P'(-1, -2), Q'(-1, 4), R'(3, 4)}\)

From Solvely APP
Source: https://solvelyapp.com/problems/17951/

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