Question

Which name best describes the polygon with vertices (0, 0), (4, 8), (12, 8), and (16, 0)? A) Triangle C) Trapezoid B) Square D) Pentagon

Answer 1

Answer:

C) Trapezoid

Step-by-step explanation:

Given

$A = (0,0)$

$B = (4,8)$

$C = (12,8)$

$D=(16,0)$

Required

The possible shape

The above are 4 vertices.

Hence, the shape cannot be

(a) Triangle ---- it has 3 vertices

(b) Pentagon ---- it has 5 vertices

Calculate distance AB using distance formula

$AB = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2$

Where:

$A = (0,0)$

$B = (4,8)$

$AB = \sqrt{(0 - 4)^2 + (0 - 8)^2$

$AB = \sqrt{( - 4)^2 + ( - 8)^2$

$AB = \sqrt{16+64$

$AB = \sqrt{80$

$AB = 8.94$

Calculate distance BC using distance formula

$BC = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2$

Where:

$B = (4,8)$

$C = (12,8)$

$BC = \sqrt{(4 - 12)^2 + (8 - 8)^2$

$BC = \sqrt{(-8)^2 + (0)^2$

$BC = \sqrt{64 +0$

$BC = \sqrt{64$

$BC = 8$

Since

$AB \ne BC$

Then, the polygon is not a square

The last available option is (c) trapezoid

Answer 2

Answer: C. Trapezoid

Step-by-step explanation:

Graph the points and you get a trapezoid!!!

Hope this helps!!!