Question
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
Determine whether the figure is a parallelogram. Justify your answer wi
the method indicated.
24.
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:
-
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 orderto form the quadrilateral. -
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.
-
-
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.