Mathematics, 21.07.2020 18:01 eshavaggar

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!

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Answer from: wdw52001

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

Answer from: Quest

answer:

given the linear inequality : $x-2y\geq -12$

add 2y to both sides we get;

$x-2y+2y\geq -12+2y$

simplify:

$x\geq -12+2y$

add 12 to both sides of an equation;

$x+12\geq -12+2y+12$

simplify:

$x+12\geq 2y$

divide both sides by 2 we get;

$\frac{x}{2} + 6 \geq y$

$y\leq \frac{x}{2} + 6$

the related equation for the inequality equation [1] is;

$y =\frac{x}{2} +6$

y-intercepts defined as the graph crosses the y-axis.

substitute x =0 in [2] to solve for y;

$y =\frac{0}{2} +6$

y = 6

x-intercepts defined as the graph crosses the x-axis.

substitute value y = 0 to solve for x;

$0 =\frac{x}{2} +6$

subtract 6 from both sides we get

$0-6 =\frac{x}{2} +6-6$

$-6 =\frac{x}{2}$

multiply both sides by 2 we get;

$-6 \times 2=x$

x = -12

now, plot these point (0, 6) and (-12, 0) on graph as shown below and shade the graph below the solid line.

Answer from: Quest

answer: the answer is graph (a)

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EQAO Watch Sammy and Pippa's teacher gives them a homework question to solve. She tells them to plot...