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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

Respuesta :

znk

Answer:

Pippa

Step-by-step explanation:

A square has

  • parallel opposite sides
  • perpendicular adjacent sides
  • perpendicular diagonals

A rhombus has  

  • parallel opposite sides
  • non-perpendicular adjacent sides
  • perpendicular diagonals

Thus, we can identify the shape by comparing the slopes of the adjacent sides.

1. Draw the shape

See the graph below

2. Calculate the slope of AB

m = (y₂ - y₁)/(x₂ - x₁) = (4 - (-1))/(9 - 5) = (4 + 1)/4 = 5/4

3. Calculate the slope of BC

If BC⟂AP, its slope should be -4/5 .

m = (y₂ - y₁)/(x₂ - x₁) = (1 - 4)/(15 - 9) =-3/6 = -1/2

½ ≠ -⅘

The two lines are not perpendicular.

Pippa is right. The shape is a rhombus.

 

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