To classify the quadrilateral LMNO using its vertices \( L(1, 1), M(2, 3), N(4, 3), O(5, 1) \), we can calculate the lengths of its sides and the slopes of its sides.
-
Calculate the lengths of the sides: \[ LM = \sqrt{(2 - 1)^2 + (3 - 1)^2} = \sqrt{1 + 4} = \sqrt{5} \] \[ MN = \sqrt{(4 - 2)^2 + (3 - 3)^2} = \sqrt{4} = 2 \] \[ NO = \sqrt{(5 - 4)^2 + (1 - 3)^2} = \sqrt{1 + 4} = \sqrt{5} \] \[ OL = \sqrt{(1 - 5)^2 + (1 - 1)^2} = \sqrt{16} = 4 \]
-
Check if opposite sides are equal (for parallelogram):
- \( LM = NO = \sqrt{5} \)
- \( MN \neq OL \) ( \(2 \neq 4\) )
Since the opposite sides are not equal, it cannot be a parallelogram.
-
Calculate the slopes of the sides: \[ \text{slope of } LM = \frac{3 - 1}{2 - 1} = \frac{2}{1} = 2 \] \[ \text{slope of } MN = \frac{3 - 3}{4 - 2} = \frac{0}{2} = 0 \] \[ \text{slope of } NO = \frac{1 - 3}{5 - 4} = \frac{-2}{1} = -2 \] \[ \text{slope of } OL = \frac{1 - 1}{1 - 5} = \frac{0}{-4} = 0 \]
- \( LM \) (slope = 2) and \( NO \) (slope = -2) are not parallel.
- \( MN \) and \( OL \) (both slopes = 0) are parallel.
Since one pair of sides is parallel, LMNO can be classified as a trapezoid.
Therefore, the answer is: Trapezoid
1 answer