What is the perimeter of the parallelogram JKLM, whose co-ordinates are J(-5,2), K (-2, 6), L (5,6), M(2, 2). 

Options

A. 30 units
B. 24 units
C. 28 units
D. 21 units

Answer

To find the perimeter of the parallelogram JKLM with given coordinates, we will follow these steps:

### Step 1: Identify the coordinates
The coordinates of the vertices of the parallelogram are:
- J(-5, 2)
- K(-2, 6)
- L(5, 6)
- M(2, 2)

### Step 2: Calculate the lengths of the sides
We will use the distance formula to calculate the lengths of the sides JK, KL, LM, and MJ. The distance formula is:
\[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \]

#### Length of JK
Using the coordinates of J and K:
\[ JK = \sqrt{((-2) - (-5))^2 + (6 - 2)^2} \]
\[ = \sqrt{(3)^2 + (4)^2} \]
\[ = \sqrt{9 + 16} = \sqrt{25} = 5 \]

#### Length of KL
Using the coordinates of K and L:
\[ KL = \sqrt{(5 - (-2))^2 + (6 - 6)^2} \]
\[ = \sqrt{(7)^2 + (0)^2} \]
\[ = \sqrt{49} = 7 \]

#### Length of LM
Using the coordinates of L and M:
\[ LM = \sqrt{(2 - 5)^2 + (2 - 6)^2} \]
\[ = \sqrt{(-3)^2 + (-4)^2} \]
\[ = \sqrt{9 + 16} = \sqrt{25} = 5 \]

#### Length of MJ
Using the coordinates of M and J:
\[ MJ = \sqrt{((-5) - 2)^2 + (2 - 2)^2} \]
\[ = \sqrt{(-7)^2 + (0)^2} \]
\[ = \sqrt{49} = 7 \]

### Step 3: Calculate the perimeter
The perimeter \( P \) of the parallelogram is the sum of the lengths of all sides:
\[ P = JK + KL + LM + MJ \]
\[ = 5 + 7 + 5 + 7 \]
\[ = 24 \]

### Final Answer
The perimeter of the parallelogram JKLM is **24 units**.

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