Final answer:
To find the perimeter of a triangle with given coordinates, calculate the distance between each pair of coordinates and add them up. The perimeter of the triangle with coordinates (-4,5), (8,5), and (8,-4) is 36 units.
Step-by-step explanation:
To find the perimeter of a triangle, we need to calculate the distance between each pair of coordinates and then add them up. Let's calculate the distance between (-4,5) and (8,5). Since the y-coordinate is the same for both points, the distance is simply the absolute difference between the x-coordinates, which is 8 - (-4) = 12 units. Next, let's calculate the distance between (8,5) and (8,-4). Since the x-coordinate is the same for both points, the distance is simply the absolute difference between the y-coordinates, which is 5 - (-4) = 9 units.
Lastly, let's calculate the distance between (8,-4) and (-4,5). We can use the distance formula, which is sqrt((x2 - x1)^2 + (y2 - y1)^2), to calculate the distance. Plugging in the values, we get sqrt((8 - (-4))^2 + (-4 - 5)^2) = sqrt(12^2 + (-9)^2) = sqrt(144 + 81) = sqrt(225) = 15 units. Finally, we add up all the distances: 12 + 9 + 15 = 36 units. Therefore, the perimeter of the triangle is 36 units. So, the correct answer is b) 36 units.