Question

EQAO Watch Sammy and Pippa's teacher gives them a homework question to solve. She tells them to plot the points A(5, -1), B(9, 4), C(15, 1) and D(11, -4) on a grid and decide whether the shape is a square or a rhombus. Sammy and Pippa do their slope calculations and Sammy insists the shape is a square whereas Pippa insists the shape is a rhombus. Who is right? Show your calculations in your reasoning!

Answer 1

Pippa is right.

Explanation:

Pippa is right because when you plot it on a graph you can see that there are no 90-degree angles and a square needs 4 of them while a rhombus has only 2 acute angles and 2 obtuse angles and that is what this shape has. That is why Pippa is right.

Answer 2

None of them are correct. The shape in their homework is a rectangle

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