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2 years ago

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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

1 answer:

kvv77 [185]2 years ago

5 0

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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