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

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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
Quadrilateral LMNO is a square.

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

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