Answer:
None of them are correct. The shape in their homework is a rectangle
Step-by-step explanation:
I would be determining my answer using Length
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
A(5, -1), B(9, 4), C(15, 1) and D(11, -4)
Side/ Length AB = A(5, -1), B(9, 4)
√(x₂-x₁)²-(y₂-y₁)²
= √(9 - 5)² + (4 - (-1))²
= √4² + 5²
= √16 + 25
= √41
Side/ Length BC = , B(9, 4), C(15, 1)
= √(x₂-x₁)²-(y₂-y₁)²
= √(15 - 9)² + ( 1 - 4)²
= √6² + -3²
= √36 + 9
= √45
Side/ Length CD = C(15, 1) and D(11, -4)
√(x₂-x₁)²-(y₂-y₁)²
= √(11 - 15)² + (-4 - 1)²
= √-4² + -5²
= √16 + 25
= √41
Side/ Length AD = A(5, -1), D(11, -4)
√(x₂-x₁)²-(y₂-y₁)²
= √(11- 5)² + (-4 - (-1))²
= √6² + 3²
= √36 + 9
= √45
From the Calculations above ,
AB = √41
BC = √45
CD = √41
AD = √45
A square and a rhombus are shapes with 4 sides and all their sides are equal to each other.
From the above calculation, we can see that
We can see that Length AB = Length CD
Length BC = Length AD
This means , the Opposite sides only are equal to each other.
Therefore, none of them is correct. The shape in their homework is a rectangle
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