Question

Which of the following best describes the figure with vertices (-8, 2), (4, 14), (16, 2) and(4, -10)? thank

Answer 1

Given:

Vertices (-8, 2), (4, 14), (16, 2) and (4, -10).

Required:

To find the figure that is made by the vertices.

Explanation:

Let A (-8, 2), B(4, 14), C(16, 2) and D(4, -10).

Then find the length of each side by using the distance formula.

$\begin{gathered} AB=\sqrt{(4+8)^2+(14-2)^2} \\ AB=\sqrt{(12)^2+(12)^2} \\ AB=\sqrt{144+144} \\ AB=12\sqrt{2} \end{gathered}$$\begin{gathered} BC=\sqrt{(16-4)^2+(2-14)^2} \\ BC=\sqrt{(12)^2+(-12)^2} \\ BC=\sqrt{144+144} \\ BC=12\sqrt{2} \end{gathered}$$\begin{gathered} CD=\sqrt{(4-16)^2+(-10-2)^2} \\ CD=\sqrt{(-12)^2+(-12)^2}^ \\ CD=\sqrt{144+144} \\ CD=12\sqrt{2} \end{gathered}$

$\begin{gathered} AD=\sqrt{(4+8)^2+(-10-2)^2} \\ AD=\sqrt{(12)^2+(-12)^2} \\ AD=\sqrt{144+144} \\ AD=12\sqrt{2} \end{gathered}$

All sides are equal.

AB =BC = CD = AD

We know that the figure in which all sides are equal is called a square.

Final Answer:

Option 2 is the correct answer.