Answer: 24 units.
Step-by-step explanation: To find the perimeter of the right triangle, you need to add up the lengths of all three sides of the triangle.
The right triangle shown has a vertex at (-4, 4), another vertex at (4, 4), and a third vertex at (4, -2). The length of the side between the first two vertices can be calculated using the distance formula:
distance = sqrt((x2 - x1)^2 + (y2 - y1)^2)
= sqrt((4 - (-4))^2 + (4 - 4)^2)
= sqrt(8^2 + 0)
= sqrt(64)
= 8
The length of the side between the second and third vertices can be calculated using the distance formula:
distance = sqrt((x2 - x1)^2 + (y2 - y1)^2)
= sqrt((4 - 4)^2 + (-2 - 4)^2)
= sqrt(0 + (-6)^2)
= sqrt(36)
= 6
The length of the hypotenuse of the right triangle can be calculated using the Pythagorean theorem:
c^2 = a^2 + b^2
c = sqrt(a^2 + b^2)
= sqrt(8^2 + 6^2)
= sqrt(64 + 36)
= sqrt(100)
= 10
To find the perimeter of the triangle, add up the lengths of all three sides: 8 + 6 + 10 = 24 units.
Therefore, the perimeter of the right triangle is 24 units.