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

Answer 1

To find the perimeter of rectangle LMNO, we need to add the lengths of all four sides.

The length of side LM is calculated as follows:
LM = distance between points L(-2, -1) and M(-5, -1)

LM = √[(-5 - (-2))^2 + (-1 - (-1))^2]
LM = √[(-3)^2 + 0^2]
LM = √[9 + 0]
LM = √9
LM = 3

The length of side MN is calculated as follows:
MN = distance between points M(-5, -1) and N(-5, -6)

MN = √[(-5 - (-5))^2 + (-6 - (-1))^2]
MN = √[0^2 + (-5)^2]
MN = √[0 + 25]
MN = √25
MN = 5

The length of side NO is calculated as follows:
NO = distance between points N(-5, -6) and O(-2, -6)

NO = √[(-2 - (-5))^2 + (-6 - (-6))^2]
NO = √[(-2 + 5)^2 + 0^2]
NO = √[3^2 + 0^2]
NO = √9
NO = 3

The length of side OL is calculated as follows:
OL = distance between points O(-2, -6) and L(-2, -1)

OL = √[(-2 - (-2))^2 + (-1 - (-6))^2]
OL = √[0^2 + (-5)^2]
OL = √[0 + 25]
OL = √25
OL = 5

Therefore, the perimeter of rectangle LMNO is:
Perimeter = LM + MN + NO + OL
Perimeter = 3 + 5 + 3 + 5
Perimeter = 16

So, the perimeter of rectangle LMNO is 16 units.