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 Paralleogram
Kite
Square
Trapezoid

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

A. Parallelogram

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