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.
kite
parallelogram
square
trapezoid

The quadrilateral is a trapezoid ⇒ 4th answer

Step-by-step explanation:

* Lets revise the properties of the figures

- The kite is a quadrilateral with perpendicular diagonals and the longest

  diagonal is the axis of symmetry of it

- Parallelogram is a quadrilateral with every two opposite sides are

 parallel or two opposite sides are parallel and equal or two diagonals

 bisect each other

- Square is a parallelogram with equal sides and equal angles or equal

 and perpendicular diagonals

- Trapezoid is a quadrilateral with only two opposite sides parallel and

  not equal

- The slope of any segment with endpoints (x1 , y1) , (x2 , y2) is

* Lets solve the problem

- The vertices of quadrilateral LMNO are:

 L (1 , 1), M (2 , 3), N (4 , 3), O (5 , 1)

- Lets find slopes of its sides

# The slope of LM

∵ L = (1 , 1) , M = (2 , 3)

∴

# The slope of MN

∵ M = (2 , 3) , N = (4 , 3)

∴

- If the slope of a segment is 0 then this segment is horizontal

∴ MN is horizontal side

# The slope of NO

∵ N = (4 , 3) , O = (5 , 1)

∴

# The slope of OL

∵ O = (5 , 1) , L = (1 , 1)

∴

∵ The slope of OL is 0

∴ OL is horizontal side

- MN and OL are horizontal sides

∴ MN // OL

- The figure can not be kite because there is no parallel sides in the kite

∵ The slopes of LM and NO are different

∴ LM and NO are not parallel

- The figure can not be parallelogram or square because in

  parallelogram and square every two opposite sides are parallel

* Lets find the length of MN and OL to be sure they are not equal

∵ MN is a horizontal side

∴ Its length is the difference between the x-coordinates of M and N

∵ x-coordinate of M = 2 and x-coordinate of N = 4

∴ The length of MN = 4 - 2 = 2

∵ OL is a horizontal side

∴ Its length is the difference between the x-coordinates of O and L

∵ x-coordinate of O = 5 and x-coordinate of L = 1

∴ The length of LO = 5 - 1 = 4

- In quadrilateral LMNO

∵ MN and OL are opposite sides

∵ MN // OL

∵ MN ≠ OL

- Two opposite sides are parallel and not equal

∴ The quadrilateral is a trapezoid

Parallelogram

Step-by-step explanation: