To calculate the slopes of the sides of quadrilateral JKLM, we can use the formula for the slope between two points \((x_1, y_1)\) and \((x_2, y_2)\):
\[ \text{slope} = \frac{y_2 - y_1}{x_2 - x_1} \]
Step 1: Calculate the slopes of each side
1. Slope of JK:
- J(−4, 1) and K(2, 3) \[ \text{slope of } JK = \frac{3 - 1}{2 - (-4)} = \frac{2}{6} = \frac{1}{3} \]
2. Slope of KL:
- K(2, 3) and L(5, −3) \[ \text{slope of } KL = \frac{-3 - 3}{5 - 2} = \frac{-6}{3} = -2 \]
3. Slope of LM:
- L(5, −3) and M(0, −5) \[ \text{slope of } LM = \frac{-5 - (-3)}{0 - 5} = \frac{-2}{-5} = \frac{2}{5} \]
4. Slope of MJ:
- M(0, −5) and J(−4, 1) \[ \text{slope of } MJ = \frac{1 - (-5)}{-4 - 0} = \frac{6}{-4} = -\frac{3}{2} \]
Step 2: Fill in the results
- The slope for JK is \( \frac{1}{3} \)
- The slope of KL is \( -2 \)
- The slope of LM is \( \frac{2}{5} \)
- The slope of MJ is \( -\frac{3}{2} \)
Step 3: Determine if JKLM is a parallelogram
To determine if quadrilateral JKLM is a parallelogram, we check if both pairs of opposite sides are parallel:
-
Sides JK and LM:
- Slope of JK: \( \frac{1}{3} \)
- Slope of LM: \( \frac{2}{5} \) (not equal, hence not parallel)
-
Sides KL and MJ:
- Slope of KL: \( -2 \)
- Slope of MJ: \( -\frac{3}{2} \) (not equal, hence not parallel)
Since neither pair of opposite sides is parallel, quadrilateral JKLM is not a parallelogram.
Final Answer
The slope for JK is C. 1/3, the slope of KL is A. -2, the slope of LM is D. 2/5, and the slope of MJ is B. -3/2. Quadrilateral JKLM F. is not a parallelogram because I. neither pair of opposite sides is parallel.