5. Carly draws quadrilateral \( J K L M \) with vertices \( J(-3,3), K(3,3), L(2,-1) \), and \( M(-2,-1) \). What is the best way to classify the quadrilateral?

1. **Plotting the Points and Observing the Sides** The vertices of quadrilateral \(JKLM\) are: - \(J(-3, 3)\) - \(K(3, 3)\) - \(L(2, -1)\) - \(M(-2, -1)\) Notice that: - Points \(J\) and \(K\) have the same \(y\)-coordinate, so segment \(JK\) is horizontal. - Points \(L\) and \(M\) have the same \(y\)-coordinate, so segment \(LM\) is horizontal. 2. **Determining Parallel Sides** Since both \(JK\) and \(LM\) are horizontal, they are parallel. This is a defining property of a trapezoid. 3. **Calculating the Lengths of the Legs** To check if the trapezoid is isosceles, we compute the lengths of the nonparallel sides: - **Length of \(JM\):** \[ JM = \sqrt{(-2 - (-3))^2 + (-1 - 3)^2} = \sqrt{(1)^2 + (-4)^2} = \sqrt{1 + 16} = \sqrt{17} \] - **Length of \(KL\):** \[ KL = \sqrt{(2 - 3)^2 + (-1 - 3)^2} = \sqrt{(-1)^2 + (-4)^2} = \sqrt{1 + 16} = \sqrt{17} \] Both legs have the same length, \(\sqrt{17}\), which means the trapezoid is isosceles. 4. **Conclusion** The quadrilateral is an isosceles trapezoid because it has one pair of parallel sides (\(JK\) and \(LM\)) and the nonparallel sides (\(JM\) and \(KL\)) are congruent. Thus, the best way to classify the quadrilateral is as an **isosceles trapezoid**.