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:
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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