Question

The coordinates of the vertices of​ quadrilateral JKLM​ are J(−4, 1), K(2, 3), L(5, −3), and M(0, −5).



Drag and drop the choices into each box to correctly complete the sentences.

The slope for ​JK¯¯¯¯¯​ is _________, the slops of LK¯¯¯¯¯​ is __________, the slops of ML¯¯¯¯¯​ is ____________, and the slop pf MJ¯¯¯¯¯​ is _________ Quadrilateral JKLM ____ a parallelogram because _________.

A. -2
B. -3/2
C. 1/3
D. 2/5
E. is
F. is not
G. both pairs of opposite sides are parallel
H. only one pair of opposite sides is parallel
I. neither pair of opposite sides is parallel

Answer 1

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**.