Question

Good morning I could really use some help with this problem please!!

Answer 1

Hello!

First, let's write the coordinates of each vertex of this parallelogram:

• A (-4, 2)

,

• B (2, 2)

,

• C (5, -2)

,

• D (-1, -2)

As line AB is parallel to the x-axis, we can find its measurement without formulas. We just need to count the number of squares from one point to the other.

So,

AB = 6 units.

We will follow the same reasoning to calculate CD (because it's also parallel to the x-axis).

CD = 6 units.

Now we have to use the formula of the distance between two points to calculate the sides BC and DA. The formula is:

`d_(A,B)=√((x_B-x_A)^2+(y_B-y_A)^2)`

As we know the formula, let's replace it with the coordinates:

BC: 5 units

`\begin{gathered} d_(B,C)=√(\left(x_C-x_B\right)^2+\left(y_C-y_B\right)^2) \\ d_(B,C)=√((5-2)^2+(-2-2)^2) \\ d_(B,C)=√(3^2+(-4)^2) \\ d_(B,C)=√(9+16) \\ d_(B,C)=√(25) \\ d_(B,C)=5\text{ units} \end{gathered}`

DA: 5 units

We can solve it using the same formula as I used to solve BC, but now I'll show you how to solve it using Pythagoras Theorem (I think it will be easier). Look:

Solving by Pythagoras, we'll obtain:

`\begin{gathered} x^2=4^2+3^2 \\ x^2=16+9 \\ x^2=25 \\ x=√(25) \\ x=5\text{ units} \end{gathered}`

Remembering: the perimeter is the sum of all the sides of a figure. So, we will have:

`\begin{gathered} P=AB+BC+CD+DA \\ P=6+5+6+5 \\ P=22\text{ units} \end{gathered}`