Question

Find the perimeter of rectangle LMNO , with vertices L(−2,−1) , M(−5,−1) , N(−5,−6) , and O(−2,−6) .

Answer 1

To find the perimeter of the rectangle LMNO, we need to find the distances between its four vertices and add them up.

The distance between two points (x1, y1) and (x2, y2) is given by the formula:
√[(x2-x1)^2 + (y2-y1)^2]

Using this formula, we can find the distances between the points:
1. LM: √[(-5 - (-2))^2 + (-1 - (-1))^2] = √[(-3)^2 + 0^2] = √9 = 3
2. MN: √[(-5 - (-5))^2 + (-6 - (-1))^2] = √[0^2 + (-5)^2] = √25 = 5
3. NO: √[(-2 - (-5))^2 + (-6 - (-6))^2] = √[3^2 + 0^2] = √9 = 3
4. OL: √[(-2 - (-2))^2 + (-6 - (-1))^2] = √[0^2 + (-5)^2] = √25 = 5

Adding up the distances:
Perimeter = LM + MN + NO + OL
Perimeter = 3 + 5 + 3 + 5
Perimeter = 16

Therefore, the perimeter of rectangle LMNO is 16 units.