A polygon is graphed on a coordinate grid. The location of each point on the polygon is represented by \( (x, y) \). The polygon is transformed using the rule \( (x, y) \rightarrow(t x, t y) \). Which statement is true? \( (8,3 C, R S, R C 3) \) F If \( t \) is greater than 1 , the image of the polygon is larger than the polygon. G If \( t \) is between 0 and 1 , the image of the polygon is congruent to the polygo H If \( t \) is greater than 1 , the image of the polygon is smaller than the polygon. \( J \) If \( t \) is between 0 and 1 , the image of the polygon is larger than the polygon.

The transformation given by the rule \( (x, y) \rightarrow (t x, t y) \) is a **scaling transformation** centered at the origin \((0, 0)\). Here's how different values of \( t \) affect the polygon: 1. **When \( t > 1 \):** - **Effect:** The polygon is scaled up. - **Result:** The image of the polygon becomes **larger** than the original polygon. 2. **When \( 0 < t < 1 \):** - **Effect:** The polygon is scaled down. - **Result:** The image of the polygon becomes **smaller** than the original polygon. 3. **When \( t = 1 \):** - **Effect:** No scaling occurs. - **Result:** The image of the polygon is **congruent** to the original polygon (unchanged in size). Let's evaluate each of the provided statements: - **F.** *If \( t \) is greater than 1, the image of the polygon is larger than the polygon.* - **True.** As explained, \( t > 1 \) scales the polygon up. - **G.** *If \( t \) is between 0 and 1, the image of the polygon is congruent to the polygon.* - **False.** When \( 0 < t < 1 \), the polygon becomes smaller, not congruent. - **H.** *If \( t \) is greater than 1, the image of the polygon is smaller than the polygon.* - **False.** Actually, the image becomes larger when \( t > 1 \). - **J.** *If \( t \) is between 0 and 1, the image of the polygon is larger than the polygon.* - **False.** The image becomes smaller, not larger. **Conclusion:** Among the given statements, **only statement F is true**. **Answer:** F. If \( t \) is greater than 1 , the image of the polygon is larger than the polygon.