Final answer:
To find the perimeter of a polygon, you need to add up the lengths of all its sides. In this case, we have the following vertices for the polygon: (1, -3), (5, 1), (-3, 4), and (5, 4). Using the distance formula, we can calculate the distances between each pair of consecutive vertices and then sum them to find the perimeter. The correct answer is 24 units.
Step-by-step explanation:
To find the perimeter of a polygon, you need to add up the lengths of all its sides. In this case, we have the following vertices for the polygon: (1, -3), (5, 1), (-3, 4), and (5, 4). We can calculate the distance between each pair of consecutive vertices using the distance formula.
The distance formula is given by: √[(x2 - x1)^2 + (y2 - y1)^2].
Using this formula, we can find the distance between (1, -3) and (5, 1) as √[(5 - 1)^2 + (1 - (-3))^2] = √[16 + 16] = √32. Similarly, we have the following distances: between (5, 1) and (-3, 4) = √[(5 - (-3))^2 + (1 - 4)^2] = √[64 + 9] = √73, between (-3, 4) and (5, 4) = √[(-3 - 5)^2 + (4 - 4)^2] = √[64 + 0] = √64 = 8, and between (5, 4) and (1, -3) = √[(5 - 1)^2 + (4 - (-3))^2] = √[16 + 49] = √65.
Adding up the distances, we get: √32 + √73 + 8 + √65 = 5.66 + 8.54 + 8 + 8.06 ≈ 30.26 units. Therefore, the correct answer is (d) 24 units.