Figure LMNO is located at L (1, 1), M (4, 4), N (7, 1), and O (4, −2). Use coordinate geometry to best classify quadrilateral LMNO.

Quadrilateral LMNO is a Parallelogram. This is because it's opposite sides are equal to each other. Step-by-step explanation: Where we have vertices (x₁, x₂)and (y₁, y₂) we use the formula: √(x₂-x₁)²-(y₂-y₁)² LMNO is located at L (1, 2) M (3, 1), N (0, 0), and O (−2, 1) Side LM = L (1, 2) M (3, 1), √(x₂-x₁)²-(y₂-y₁)² √(3-1)² + (1 - 2)² √ 2² + 1² √4 + 1 = √5 Side MN = M (3, 1), N (0, 0), √(x₂-x₁)²-(y₂-y₁)² √(0 -3)² + (0 - 1)² √3² + 1² √10 Side NO = N (0, 0), O (−2, 1) √(x₂-x₁)²-(y₂-y₁)² √(-2 -0)² + (1 - 0)² √(-2²) + (1)² √4 + 1 √5 Side LO = L (1, 2) , O (−2, 1,) √(x₂-x₁)²-(y₂-y₁)² √(-2-1)² + (1 - 2)² √(-3)² +(-1)² √ 9 + 1 √10 From the above calculation, we can see that LM = √5 MN = √10 NO = √5 LO = √10 In Quadrilateral LMNO LM is the opposite side of NO MN is the opposite side of LO In the calculation above, LM = NO and MN = LO This means the shape above is a Parallelogram, where the opposite sides are equal to each other

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