The lengths of the sides are 5, 3, and 4. The sum of the lengths of all three sides is 12, so the circumference of the triangle is 12 units.
To find the circumference of a triangle, we first need to determine if the given points (-4,0), (-1,-4), and (-4,-4) form a triangle. We can do this by calculating the lengths of each side of the triangle and checking if the sum of any two sides is greater than the third side. Let's calculate the lengths of the sides:
Side AB: Using the distance formula, d = sqrt((x2 - x1)^2 + (y2 - y1)^2), we have d = sqrt((-1 - (-4))^2 + (-4 - 0)^2) = sqrt(3^2 + (-4)^2) = sqrt(9 + 16) = sqrt(25) = 5
Side BC: d = sqrt((-4 - (-1))^2 + (-4 - (-4))^2) = sqrt((-3)^2 + 0^2) = sqrt(9) = 3
Side AC: d = sqrt((-4 - (-4))^2 + (-4 - 0)^2) = sqrt(0^2 +16) = sqrt(16) = 4
Now, we check if the sum of any two sides is greater than the third side:
AB + BC = 5 + 3 = 8, which is greater than AC = 4.
AB + AC = 5 + 4 = 9, which is greater than BC = 3.
BC + AC = 3 + 4 = 7, which is less than AB = 5.
Since the condition is met for AB + BC and AB + AC, but not for BC + AC, the given points form a triangle.
Next, we calculate the circumference of the triangle. Since we have the lengths of all three sides, we add them together: 5 + 3 + 4 = 12.
Therefore, the circumference of the triangle is 12 units.
The probable question may be:
In the fourth quadrant the triangles has the points (-4,0), (-1,-4), (-4,-4). Find the circumference of the triangle