1. **State the problem:** We need to classify triangle $\triangle WXY$ with vertices $W(-7,1)$, $X(0,-4)$, and $Y(2,3)$ as equilateral, isosceles, scalene, or none of the above. 2. **Formula used:** To classify a triangle by its sides, calculate the lengths of each side using the distance formula: $$d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$$ 3. **Calculate side lengths:** - Length $WX$: $$\sqrt{(0 - (-7))^2 + (-4 - 1)^2} = \sqrt{7^2 + (-5)^2} = \sqrt{49 + 25} = \sqrt{74}$$ - Length $XY$: $$\sqrt{(2 - 0)^2 + (3 - (-4))^2} = \sqrt{2^2 + 7^2} = \sqrt{4 + 49} = \sqrt{53}$$ - Length $WY$: $$\sqrt{(2 - (-7))^2 + (3 - 1)^2} = \sqrt{9^2 + 2^2} = \sqrt{81 + 4} = \sqrt{85}$$ 4. **Compare side lengths:** - $WX = \sqrt{74} \approx 8.60$ - $XY = \sqrt{53} \approx 7.28$ - $WY = \sqrt{85} \approx 9.22$ Since all three side lengths are different, the triangle has no equal sides. 5. **Conclusion:** The triangle $\triangle WXY$ is **scalene** because all sides have different lengths. **Final answer:** Scalene