K(-5, -1), L(-2, 4), M(3, 1), NO. 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.

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.

The precise name for KLMN is either a square or a rhombus

Step-by-step 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.

answer:

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