Final answer:
The perimeter of rectangle JKLM is calculated using the distance formula to find the lengths of sides JK and JM. With JK being 5 units and JM being 8 units, the perimeter is 2 times the length plus 2 times the width, resulting in a total perimeter of 26 units.
Step-by-step explanation:
To find the perimeter of rectangle JKLM with the given vertices J(-6,4), K(-6, -1), L(2, -1), M(2,4), we can calculate the distances of adjacent sides and double them, since opposite sides of a rectangle are equal in length. To calculate the distance between two points, we use the distance formula d = √((x2-x1)² + (y2-y1)²).
First, let's find the lengths of JK and JM:
JK = √((-6+6)² + (4+1)²) = √(0 + 25) = 5 units
JM = √((2+6)² + (4-4)²) = √(64 + 0) = 8 units
The perimeter (P) of a rectangle is given by the formula P = 2l + 2w, where l is the length and w is the width. We've just calculated that the length (JK) is 5 units and the width (JM) is 8 units. Therefore, the perimeter is:
P = 2 × 5 units + 2 × 8 units = 10 units + 16 units = 26 units.
The perimeter of rectangle JKLM is 26 units.