Question 3 (1 point) (04.01 MC) Figure LMNO is located at \( L(1,1), M(4,4), N(7,1) \), and \( O(4,-2) \). Use coordinate geometry to best classify quadrilateral LMNO. a Kite b Parallelogram c Square đ Trapezoid

To classify quadrilateral LMNO with vertices \( L(1,1) \), \( M(4,4) \), \( N(7,1) \), and \( O(4,-2) \), we can analyze the side lengths and slopes: 1. **Calculate Side Lengths:** - **LM:** \(\sqrt{(4-1)^2 + (4-1)^2} = \sqrt{9 + 9} = \sqrt{18}\) - **MN:** \(\sqrt{(7-4)^2 + (1-4)^2} = \sqrt{9 + 9} = \sqrt{18}\) - **NO:** \(\sqrt{(4-7)^2 + (-2-1)^2} = \sqrt{9 + 9} = \sqrt{18}\) - **OL:** \(\sqrt{(1-4)^2 + (1-(-2))^2} = \sqrt{9 + 9} = \sqrt{18}\) All sides are equal in length, suggesting a rhombus or square. 2. **Calculate Slopes:** - **Slope LM:** \( \frac{4-1}{4-1} = 1 \) - **Slope MN:** \( \frac{1-4}{7-4} = -1 \) - **Slope NO:** \( \frac{-2-1}{4-7} = 1 \) - **Slope OL:** \( \frac{1-(-2)}{1-4} = -1 \) Adjacent sides have slopes that are negative reciprocals, indicating perpendicularity. Hence, all angles are right angles. 3. **Check Diagonals:** - **Diagonal LN:** Length \(6\) and slope \(0\) (horizontal). - **Diagonal MO:** Length \(6\) and undefined slope (vertical). The diagonals are equal in length and perpendicular, confirming that the quadrilateral is a square. **Answer:** c Square