Final answer:
To find the perimeter of a triangle, we need to find the lengths of all three sides. Using the distance formula, we can calculate the lengths by substituting the coordinates of the points into the formula. Then, we add up the lengths of the three sides to find the perimeter. In this case, the perimeter of the triangle with points (2,3), (2,3), and (-1,-1) is 15 units.
Step-by-step explanation:
The perimeter of a triangle can be found by adding the lengths of all three sides. To find the length of a side, we can use the distance formula, which is:
d = √((x2 - x1)^2 + (y2 - y1)^2)
Using the given points (2,3) and (-1,-1), we can find the lengths of each side:
- Side 1: d = √((2 - -1)^2 + (3 - -1)^2) = √(3^2 + 4^2) = √(9 + 16) = √25 = 5
- Side 2: d = √((2 - -1)^2 + (3 - -1)^2) = √(3^2 + 4^2) = √(9 + 16) = √25 = 5
- Side 3: d = √((-1 - 2)^2 + (-1 - 3)^2) = √((-3)^2 + (-4)^2) = √(9 + 16) = √25 = 5
Therefore, the perimeter of the triangle is 5 + 5 + 5 = 15 units.