Question

question 12(multiple choice worth 1 points) (04.01 mc) figure lmno is located at l(1, 1), m(2, 3), n(4, 3), and o(5, 1). use coordinate geometry to best classify quadrilateral lmno. o kite o parallelogram o square o trapezoid

Explanation:

Step1: Calculate side - lengths

Use the distance formula $d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$.
For side LM with $L(1,1)$ and $M(2,3)$:
$LM=\sqrt{(2 - 1)^2+(3 - 1)^2}=\sqrt{1 + 4}=\sqrt{5}$
For side MN with $M(2,3)$ and $N(4,3)$:
$MN=\sqrt{(4 - 2)^2+(3 - 3)^2}=\sqrt{4+0} = 2$
For side NO with $N(4,3)$ and $O(5,1)$:
$NO=\sqrt{(5 - 4)^2+(1 - 3)^2}=\sqrt{1 + 4}=\sqrt{5}$
For side OL with $O(5,1)$ and $L(1,1)$:
$OL=\sqrt{(1 - 5)^2+(1 - 1)^2}=\sqrt{16+0}=4$

Step2: Check for parallel sides

The slope formula is $m=\frac{y_2 - y_1}{x_2 - x_1}$.
Slope of LM, $m_{LM}=\frac{3 - 1}{2 - 1}=2$
Slope of NO, $m_{NO}=\frac{1 - 3}{5 - 4}=- 2$
Slope of MN, $m_{MN}=\frac{3 - 3}{4 - 2}=0$
Slope of OL, $m_{OL}=\frac{1 - 1}{1 - 5}=0$
Since $m_{MN}=m_{OL}=0$, $MN\parallel OL$.
The figure has one pair of parallel sides.

Answer:

Trapezoid