To determine the perimeter of rectangle $KLMN$, we need to find the lengths of its sides.

Step 1: Identify coordinates

From the graph:

• $K(-7, 8)$
• $L(-2, 8)$
• $M(-2, 3)$
• $N(-7, 3)$

Step 2: Calculate side lengths

1. Horizontal side ($KL$ or $NM$): Distance formula between $K(-7, 8)$ and $L(-2, 8)$: $KL = |x_2 - x_1| = |-2 - (-7)| = 5$

2. Vertical side ($KN$ or $LM$): Distance formula between $K(-7, 8)$ and $N(-7, 3)$: $KN = |y_2 - y_1| = |3 - 8| = 5$

Step 3: Calculate perimeter

The perimeter of a rectangle is given by: $P = 2 \times (\text{Length} + \text{Width})$ Substituting $\text{Length} = 5$ and $\text{Width} = 5$: $P = 2 \times (5 + 5) = 2 \times 10 = 20$

Final Answer:

The perimeter of rectangle $KLMN$ is 20 units.

Would you like more details or explanations?
Here are some additional related questions:

1. How is the distance formula derived?
2. What is the area of rectangle $KLMN$?
3. Can you find the midpoint of one of the sides?
4. How does changing one coordinate affect the perimeter?
5. What is the significance of absolute values in the distance formula?

Tip: Always ensure all points are labeled correctly to avoid errors when calculating distances.