Given the coordinates of the points, we can determine the distances between each pair of consecutive points to find the perimeter of the polygon. We'll use the distance formula:
\[
d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}
\]
Here are the coordinates for the points:
- \(A(2, -6)\)
- \(B(-5, -6)\)
- \(C(-5, 6)\)
- \(D(6, 6)\)
- \(E(6, 1)\)
- \(F(2, 1)\)
Let's calculate each segment:
1. Distance \( AB \) from \( A(2, -6) \) to \( B(-5, -6) \):
\[
d_{AB} = \sqrt{(-5 - 2)^2 + (-6 - (-6))^2} = \sqrt{(-7)^2 + 0} = \sqrt{49} = 7
\]
2. Distance \( BC \) from \( B(-5, -6) \) to \( C(-5, 6) \):
\[
d_{BC} = \sqrt{(-5 - (-5))^2 + (6 - (-6))^2} = \sqrt{0 + 12^2} = \sqrt{144} = 12
\]
3. Distance \( CD \) from \( C(-5, 6) \) to \( D(6, 6) \):
\[
d_{CD} = \sqrt{(6 - (-5))^2 + (6 - 6)^2} = \sqrt{11^2 + 0} = \sqrt{121} = 11
\]
4. Distance \( DE \) from \( D(6, 6) \) to \( E(6, 1) \):
\[
d_{DE} = \sqrt{(6 - 6)^2 + (1 - 6)^2} = \sqrt{0 + (-5)^2} = \sqrt{25} = 5
\]
5. Distance \( EF \) from \( E(6, 1) \) to \( F(2, 1) \):
\[
d_{EF} = \sqrt{(2 - 6)^2 + (1 - 1)^2} = \sqrt{(-4)^2 + 0} = \sqrt{16} = 4
\]
6. Distance \( FA \) from \( F(2, 1) \) to \( A(2, -6) \):
\[
d_{FA} = \sqrt{(2 - 2)^2 + (-6 - 1)^2} = \sqrt{0 + (-7)^2} = \sqrt{49} = 7
\]
Adding these distances together gives the perimeter of the polygon:
\[
\text{Perimeter} = d_{AB} + d_{BC} + d_{CD} + d_{DE} + d_{EF} + d_{FA} = 7 + 12 + 11 + 5 + 4 + 7 = 46 \text{ units}
\]
Since the problem asks for the perimeter in kilometers and no conversion factor is given, we assume the units directly correspond:
\[
\text{Perimeter} = 46 \text{ kilometers}
\]
Use the image to answer the question.
A coordinate plane shows the x-axis ranging from negative 9 to 9 in unit increments and the y-axis ranging from negative 11 to 11 in unit increments. Six plotted points are joined to form a composite figure. The six plotted points are upper A, upper B, upper C, upper D, upper E, and upper F. The coordinates of the plotted points are as follows: point upper A is left parenthesis 2 comma negative 6 right parenthesis, point upper B is left parenthesis negative 5 comma negative 6 right parenthesis, point upper C is left parenthesis negative 5 comma 6 right parenthesis, point upper D is left parenthesis 6 comma 6 right parenthesis, point upper E is left parenthesis 6 comma 1 right parenthesis, and point upper F is left parenthesis 2 comma 1 right parenthesis.
Find the perimeter of the polygon in kilometers.
1 answer