Question

1. abcdef is a regular hexagon with vertex a(-7, 0) and b(-3, 3). tyrone finds that abcdef has a perimeter of 30 units. is tyrone correct? explain and show work to support your answer.

Explanation:

Step1: Calculate length of AB

Use distance formula $d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$. For $A(-7, 0)$ and $B(-3, 3)$:
$d = \sqrt{(-3 - (-7))^2 + (3 - 0)^2} = \sqrt{(4)^2 + (3)^2} = \sqrt{16 + 9} = \sqrt{25} = 5$.

Step2: Find perimeter of regular hexagon

A regular hexagon has 6 equal sides. Perimeter $P = 6 \times$ side length. Here, side length $AB = 5$, so $P = 6 \times 5 = 30$.

Answer:

Tyrone is correct because the length of side \( AB \) is 5 units (calculated via the distance formula), and a regular hexagon with 6 equal sides of length 5 has a perimeter of \( 6 \times 5 = 30 \) units.