This question is incomplete because it was not written correctly.
Complete Question:
K(-5, -1), L(-2, 4), M(3, 1), N(-2, 4)
Determine the most precise name for KLMN (parallelogram, rhombus, rectangle, or square). Explain how you determined your answer. You must support your answer using length or slope.
Answer:
The precise name for KLMN is either a square or a rhombus
Explanation:
To find the length of the sides, when you have vertices (x₁, x₂)and (y₁, y₂) we use the formula
√(x₂-x₁)²-(y₂-y₁)²
K(-5, -1), L(-2, 4), M(3, 1), N(-2, 4)
Side/ Length KL = K(-5, -1), L(-2, 4)
= √(x₂-x₁)²-(y₂-y₁)²
= √(-2 -(- 5))² + (4 - (-1))²
= √3² + 5²
= √9 + 25
= √34
Side/ Length LM = L(-2, 4), M(3, 1),
= √(x₂-x₁)²-(y₂-y₁)²
= √(3 - (-2))² + ( 1 - 4)²
= √5² + -3²
= √25 + 9
= √34
Side/ Length MN = M(3, 1), N(-2, 4)
√(x₂-x₁)²-(y₂-y₁)²
= √(-2 - 3)² + (4 - 1)²
= √-5² + 3²
= √25 + 9
= √34
Side/ Length KN = K(-5, -1), N(-2, 4)
√(x₂-x₁)²-(y₂-y₁)²
= √(- 2 -(- 5)² + (4 - (-1))²
= √3² + 5²
= √9 + 25
= √34
From the above calculation, we can see that
KL = √34
LM = √34
MN = √34
KN = √34
This means Length KL = LM = MN = KN
This shape is a Square and a Rhombus. This reason is a square and a rhombus are Quadrilateral shapes whose sides are equal to each other.