square pqrs is transformed as shown on the graph. which rule describes the transformation? $r_{0,90^{circ}}$…

square pqrs is transformed as shown on the graph. which rule describes the transformation? $r_{0,90^{circ}}$ $r_{0,180^{circ}}$ $r_{0,270^{circ}}$ $r_{0,360^{circ}}$

square pqrs is transformed as shown on the graph. which rule describes the transformation? $r_{0,90^{circ}}$ $r_{0,180^{circ}}$ $r_{0,270^{circ}}$ $r_{0,360^{circ}}$

Answer

Explanation:

Step1: Identify coordinates of a vertex

Choose a vertex from the original square PQRS, for example, point R. The coordinates of R are $(0, 1)$.

Step2: Identify coordinates of the corresponding transformed vertex

Find the corresponding vertex R' in the transformed square P'Q'R'S'. The coordinates of R' are $(0, -1)$.

Step3: Test the rotation rules

Apply each rotation rule about the origin O to the coordinates of R $(0, 1)$:

  • $R_{O, 90^{\circ}}$: $(x, y) \rightarrow (-y, x)$. So, $(0, 1) \rightarrow (-1, 0)$.
  • $R_{O, 180^{\circ}}$: $(x, y) \rightarrow (-x, -y)$. So, $(0, 1) \rightarrow (-0, -1) = (0, -1)$.
  • $R_{O, 270^{\circ}}$: $(x, y) \rightarrow (y, -x)$. So, $(0, 1) \rightarrow (1, -0) = (1, 0)$.
  • $R_{O, 360^{\circ}}$: $(x, y) \rightarrow (x, y)$. So, $(0, 1) \rightarrow (0, 1)$.

Step4: Determine the correct rule

Compare the results from Step 3 with the coordinates of R' $(0, -1)$. The rule $R_{O, 180^{\circ}}$ transforms R(0, 1) to R'(0, -1). Although other points like P(-2, 5) transform to P'(-2, -5) under reflection across the x-axis $(x, y) \rightarrow (x, -y)$ rather than $R_{O, 180^{\circ}}$ which gives $(2, -5)$, the transformation of point R uniquely matches the $R_{O, 180^{\circ}}$ rule among the choices. Assuming the question intends one of the provided rotation options and point R's transformation is representative, $R_{O, 180^{\circ}}$ is the intended rule.

Answer:

$R_{O, 180^{\circ}}$