The perimeter of a polygon is simply the sum of the lengths of all its sides. In this case, we have a triangle, so we'll find the lengths of three sides and sum them up to find the perimeter.
Step 1: Find the length of line segment JK.
The length of a segment between two points in 2-dimensional space can be found using the formula sqrt((x2-x1)^2 + (y2-y1)^2), where (x1,y1) and (x2,y2) are the coordinates of the two points. Using this formula, the length of line segment JK is found as follows:
sqrt((5-(-1))^2 + (3-3)^2) = 6.0 units.
Step 2: Find the length of line segment KL.
Similarly, we use the same formula to find the length of line segment KL as follows:
sqrt((2-5)^2 + ((-2)-3)^2) = 5.830951894845301 units.
Step 3: Find the length of line segment LJ.
Applying the formula, the length of line segment LJ is:
sqrt((2-(-1))^2 + ((-2)-3)^2) = 5.830951894845301 units.
Step 4: Sum up the lengths of all three sides to find the perimeter of the triangle.
The perimeter of the triangle is then found by adding up the lengths of all three sides:
6.0 + 5.830951894845301 + 5.830951894845301 = 17.6619037896906 units.
So the perimeter of the triangle JKL with vertices J(-1,3) K(5,3) L(2,-2) is approximately 17.66 units.