Question

Find the perimeter of the polygon with the vertices G(2,4), H(2,-3), J(-2,-3), and K(-2,4).

a) 20 units

b) 16 units

c) 14 units

d) 18 units

Answer 1

2(4 - (-3)) + 2(2 - (-2)) = 2(7) + 2(4) = 22

Answer 2

After calculating the lengths of the sides of the rectangle formed by vertices G, H, J, and K, the perimeter is found to be 22 units, which does not match any of the given answer choices.

Step-by-step explanation:

The question asks us to find the perimeter of a polygon with given vertices. This polygon, by the coordinates given, is a rectangle. We can find the lengths of the sides by subtracting the coordinates of the vertices. The length of GH or JK is the difference in the y-coordinates (4 - (-3) = 7 units). The length of GJ or HK is the difference in the x-coordinates (2 - (-2) = 4 units). Since the opposite sides of a rectangle are equal, we multiply the lengths by 2 and add them to find the perimeter:

P = 2 * (GH + GJ) = 2 * (7 units + 4 units) = 2 * 11 units = 22 units.

However, none of the answer choices match this result, suggesting there may have been a typo in the question or choices. Among the given options, none accurately represent the calculated perimeter.