Question

The coordinates of the vertices of a polygon are (−2,−2), (3,−3), (4,−6), (1,−6), and (−2,−4).

Answer 1

The perimeter of the polygon to the nearest tenth of a unit  $\boxed{16.9{\text{ units}}}.$ Option (b) is correct.

Further explanation:

The distance between the two points can be calculated as follows,

$\boxed{{\text{Distance}}=\sqrt {{{\left( {{x_2} - {x_1}} \right)}^2} + {{\left( {{y_2} - {y_1}} \right)}^2}}}$

Given:

The coordinates of the vertices of the polygon are $\left({ - 2, - 2}\right),\left( {3, - 3}\right),\left( {4, - 6}\right),\left( {1, - 6}\right)$ and $\left( { - 2, - 4}\right).$

Explanation:

Consider the points as A $\left( { - 2, - 2} \right), B\left( {3, - 3} \right), C\left( {4, - 6} \right), D\left( {1, - 6} \right)$ and  $E\left({ - 2, - 4} \right).$

The distance between point A and point B can be calculated as follows,

$\begin{aligned}{\text{Distance}}&=\sqrt {{{\left( {3 + 2} \right)}^2} + {{\left( { - 3 + 2}\right)}^2}}\\ &= \sqrt {25 + 1}\\&= \sqrt {26}\\&= 5.2\\\end{aligned}$

The distance between point B and point C can be calculated as follows,

$\begin{aligned}{\text{Distance}}&=\sqrt {{{\left( {4 - 3} \right)}^2} + {{\left( { - 6 + 3} \right)}^2}}\\&= \sqrt {{1^2} + 9}\\&= \sqrt {10}\\&= 3.17\\\end{aligned}$

The distance between point C and point D can be calculated as follows,

$\begin{aligned}{\text{Distance}}&= \sqrt {{{\left({1 - 4} \right)}^2} + {{\left( { - 6 + 6}\right)}^2}} \\&=\sqrt {{3^2} + 0}\\&= \sqrt9\\&= 3\\\end{aligned}$

The distance between point D and point E can be calculated as follows,

$\begin{aligned}{\text{Distance}}&= \sqrt {{{\left( { - 2 - 1}\right)}^2} + {{\left( { - 4 + 6}\right)}^2}}\\&= \sqrt{ - {3^2} + {2^2}}\\&= \sqrt {9 + 4}\\&= \sqrt {13}\\&= 3.61\\\end{aligned}$

The distance between point E and point A can be calculated as follows,

$\begin{aligned}{\text{Distance}} &= \sqrt {{{\left( { - 2 + 2} \right)}^2} + {{\left( { - 4 + 2} \right)}^2}}\\ &= \sqrt {{0^2} + {2^2}}\\&=\sqrt4\\&= 2\\\end{aligned}$

The perimeter of the polygon can be calculated as follows,

$\begin{aligned}{\text{Perimeter}}&= 5.12 + 3.17 + 3 + 3.61 + 2\\&= 16.9\\\end{aligned}$

Option (a) is not correct.

Option (b) is correct.

Option (c) is not correct.

Option (d) is not correct.

The perimeter of the polygon to the nearest tenth of a unit $\boxed{16.9{\text{ units}}}.$ Option (b) is correct.

Learn more:

1. Learn more about inverse of the functionhttps://brainly.com/question/1632445.

2. Learn more about equation of circle brainly.com/question/1506955.

3. Learn more about range and domain of the function brainly.com/question/3412497

Answer details:

Grade: High School

Subject: Mathematics

Chapter: Coordinate geometry

Keywords: Coordinates, vertices, polygon, x-coordinate, y-coordinate, perimeter, circumference, nearest tenth unit, distance formula.

Answer 2

The perimeter of the polygon is 17.5