Question

Which of the following shows that the quadrilateral with vertices L (0,4), M (3,5), N (2,1), and 0 (-1,0) is a parallelogram? A. Slope of LM = slope of NO = 1/3; Slope of MN = slope of LO = 4/1; since both pairs of opp. sides are || LMNO is a parallelogram by definition. B. Slope of LM = slope of NO = 1/3; Slope of MN = slope of LO = -4/1; since both pairs of opp. sides are || , LMNO is a parallelogram by definition. C. Slope of LM = slope of NO = -4/1; Slope of MN = slope of LO = -1/3; since both pairs of opp. sides are || , LMNO is a parallelogram by definition. D. Slope of LM = slope of NO = -1/3; Slope of MN = slope of LO = 1/4; since both pairs of opp. sides are ||, LMNO is a parallelogram by definition.

Answer 1

To determine if the quadrilateral with vertices L (0,4), M (3,5), N (2,1), and O (-1,0) is a parallelogram, we compare the slopes of the opposite sides and find that they are equal. Therefore, the quadrilateral is a parallelogram.

Step-by-step explanation:

In order to determine if the quadrilateral with vertices L (0,4), M (3,5), N (2,1), and O (-1,0) is a parallelogram, we need to compare the slopes of the opposite sides. Let's calculate the slopes:

1. Slope of LM = (5-4)/(3-0) = 1/3

2. Slope of NO = (0-1)/(-1-2) = 1/3

3. Slope of MN = (1-5)/(2-3) = -4/1 = -4

4. Slope of LO = (4-0)/(0-(-1)) = 4/1 = 4

The slopes of LM and NO are equal, and the slopes of MN and LO are equal. Since both pairs of opposite sides have equal slopes, the quadrilateral LMNO is a parallelogram by definition. Therefore, the correct option is A.

Answer 2

After calculating the slopes of the sides of the quadrilateral LMNO, it's evident that opposite sides have equal slopes, indicating that they are parallel. This confirms that LMNO is a parallelogram by definition.

Step-by-step explanation:

To determine whether the quadrilateral with vertices L (0,4), M (3,5), N (2,1), and O (-1,0) is a parallelogram, we need to compare the slopes of opposite sides. The slope of a line is given by the change in y over the change in x (rise over run).

Let's calculate the slopes:

• 
  
• Slope of LM = (5 - 4) / (3 - 0) = 1 / 3
• 
  
• Slope of NO = (0 - 1) / (-1 - 2) = 1 / 3
• 
  
• Slope of MN = (1 - 5) / (2 - 3) = -4 / 1
• 
  
• Slope of LO = (0 - 4) / (-1 - 0) = -4 / 1

Since the slopes of LM and NO are equal, as well as the slopes of MN and LO, we can say that both pairs of opposite sides are parallel. Therefore, by definition, LMNO is a parallelogram.

Thus, the correct answer is:

B. Slope of LM = slope of NO = 1/3; Slope of MN = slope of LO = -4/1; since both pairs of opp. sides are parallel, LMNO is a parallelogram by definition.