Question

Find the perimeter of rectangle LMNO , with vertices L(−2,−1) , M(−5,−1) , N(−5,−6) , and O(−2,−6) .(1 point) Responses 24 units 24 units 16 units 16 units 15 units 15 units 20 units

Answer 1

To find the perimeter of rectangle LMNO with vertices \( L(-2, -1) \), \( M(-5, -1) \), \( N(-5, -6) \), and \( O(-2, -6) \), we first need to determine the lengths of the sides.

1. **Calculate the length of side LM:**
Since points L and M have the same y-coordinate, the distance between them is simply the difference in their x-coordinates:
\[
LM = |x_M - x_L| = |-5 - (-2)| = |-5 + 2| = |-3| = 3 \text{ units}
\]

2. **Calculate the length of side LN:**
Similarly, points L and N have the same x-coordinate, so we find the distance by taking the difference in their y-coordinates:
\[
LN = |y_N - y_L| = |-6 - (-1)| = |-6 + 1| = |-5| = 5 \text{ units}
\]

3. **Calculate the perimeter of rectangle LMNO:**
The perimeter \( P \) of a rectangle is given by the formula:
\[
P = 2 \times (length + width) = 2 \times (LM + LN)
\]
Substituting the values we found:
\[
P = 2 \times (3 + 5) = 2 \times 8 = 16 \text{ units}
\]

Thus, the perimeter of rectangle LMNO is **16 units**.