Question

figure lmno is located at l (1, 2) m (3, 1), n (0, 0), and o (-2, 1). use coordinate geometry to best classify quadrilateral lmno. parallelogram kite square trapezoid

Explanation:

Step1: Calculate the slopes of the sides

The slope formula is \(m = \frac{y_2 - y_1}{x_2 - x_1}\).
For \(LM\) with \(L(1,2)\) and \(M(3,1)\):
\(m_{LM}=\frac{1 - 2}{3 - 1}=\frac{-1}{2}=-\frac{1}{2}\)
For \(NO\) with \(N(0,0)\) and \(O(-2,1)\):
\(m_{NO}=\frac{1 - 0}{-2 - 0}=-\frac{1}{2}\)
For \(MN\) with \(M(3,1)\) and \(N(0,0)\):
\(m_{MN}=\frac{0 - 1}{0 - 3}=\frac{1}{3}\)
For \(OL\) with \(O(-2,1)\) and \(L(1,2)\):
\(m_{OL}=\frac{2 - 1}{1-(-2)}=\frac{1}{3}\)

Step2: Check the properties of quadrilaterals

Since \(m_{LM}=m_{NO}\) and \(m_{MN}=m_{OL}\), opposite sides are parallel.
A parallelogram is a quadrilateral with both pairs of opposite sides parallel.
A kite has two pairs of adjacent sides equal.
A square has all sides equal and all angles \(90^{\circ}\) (slopes of adjacent sides would be negative - reciprocals, but \(m_{LM}\times m_{MN}=(-\frac{1}{2})\times\frac{1}{3}=-\frac{1}{6}
eq - 1\)).
A trapezoid has only one pair of parallel sides.

Answer:

Parallelogram