Question

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

Answer 1

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

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.