1. **Problem Statement:** We have triangle RNA with vertices R(-5,7), N(-2,3), and A(-7,3). It is rotated 270 degrees clockwise about the origin to form triangle R'N'A'. We need to determine which statement about the triangles is true. 2. **Rotation Rule:** A 270-degree clockwise rotation about the origin transforms a point $(x,y)$ to $(y,-x)$. 3. **Apply Rotation:** - $R(-5,7) \to R'(7,5)$ - $N(-2,3) \to N'(3,2)$ - $A(-7,3) \to A'(3,7)$ 4. **Check Side Lengths:** Calculate side lengths of RNA: - $RN = \sqrt{(-2+5)^2 + (3-7)^2} = \sqrt{3^2 + (-4)^2} = \sqrt{9+16} = 5$ - $NA = \sqrt{(-7+2)^2 + (3-3)^2} = \sqrt{(-5)^2 + 0} = 5$ - $AR = \sqrt{(-7+5)^2 + (3-7)^2} = \sqrt{(-2)^2 + (-4)^2} = \sqrt{4+16} = \sqrt{20} = 2\sqrt{5}$ Calculate side lengths of R'N'A': - $R'N' = \sqrt{(3-7)^2 + (2-5)^2} = \sqrt{(-4)^2 + (-3)^2} = 5$ - $N'A' = \sqrt{(3-3)^2 + (7-2)^2} = \sqrt{0 + 5^2} = 5$ - $A'R' = \sqrt{(7-3)^2 + (5-7)^2} = \sqrt{4^2 + (-2)^2} = \sqrt{16+4} = \sqrt{20} = 2\sqrt{5}$ 5. **Conclusion:** The side lengths of triangle RNA are equal to the corresponding side lengths of triangle R'N'A'. Since rotation is a rigid transformation, the triangles are congruent, and their areas and perimeters are equal. **Final answer:** The side lengths of triangle RNA are equal to the corresponding side lengths of triangle R'N'A'.