Question
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DOROINATE GEOMETRY Graph each quadrilateral with the given vertice
Determine whether the figure is a parallelogram. Justify your answer wi
the method indicated.
24. ; Slope Formula

Ask by Pierce Mathis. in the United States
Jan 23,2025

Upstudy AI Solution

Tutor-Verified Answer

Answer

The quadrilateral with vertices , , , and is a parallelogram because both pairs of opposite sides are parallel.

Solution

To determine whether the quadrilateral with vertices , , , and is a parallelogram, we’ll follow these steps:
  1. Graph the Quadrilateral:
    While I can’t provide a visual graph here, you can plot the points on a coordinate plane:
    • A(-3, 4): 3 units left of the origin and 4 units up.
    • B(4, 5): 4 units right of the origin and 5 units up.
    • C(5, -1): 5 units right of the origin and 1 unit down.
    • D(-2, -2): 2 units left of the origin and 2 units down.
    Connect the points in the order to form the quadrilateral.
  2. Determine if is a Parallelogram Using the Slope Formula:
    A quadrilateral is a parallelogram if both pairs of opposite sides are parallel. To check for parallelism, we’ll calculate the slopes of opposite sides using the slope formula:
    • Slope of :
    • Slope of :
      Since , sides and are parallel.
    • Slope of :
    • Slope of :
      Since , sides and are parallel.
  3. Conclusion:
    Both pairs of opposite sides ( & , and & ) are parallel because they have equal slopes. Therefore, the quadrilateral is a parallelogram.

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Beyond the Answer

To graph the quadrilateral with vertices A(-3,4), B(4,5), C(5,-1), and D(-2,-2), plot each point on a coordinate plane and connect them in order. You’ll see a figure that resembles a skewed quadrilateral! Using the slope formula , find the slopes of segments AB, BC, CD, and DA to determine if opposite sides are parallel.
Upon calculating the slopes:
  • Slope AB =
  • Slope BC =
  • Slope CD =
  • Slope DA =
Since the slopes of AB and CD are equal ( ) and the slopes of BC and DA are equal (-6), you can conclude that the figure is a parallelogram because both pairs of opposite sides have equal slopes, which confirms they are parallel.

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