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What kind of a quadrilateral is formed by the vertices (0, 0), (4, 3), (3, 5) and (-1, 2)?
- a)square
- b)Rectangle
- c)Parallelogram
- d)Equilateral quadrilateral
Correct answer is option 'C'. Can you explain this answer?
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Most Upvoted Answer
What kind of a quadrilateral is formed by the vertices (0, 0), (4, 3),...
Given Quadrilateral:
A = (0, 0)
B = (4, 3)
C = (3, 5)
D = (-1, 2)
To determine the type of quadrilateral formed by these vertices, we need to analyze the properties of the sides and angles.
Step 1: Calculate the lengths of the sides
Using the distance formula, we can find the length of each side of the quadrilateral:
AB = √((4-0)^2 + (3-0)^2) = √(16+9) = √25 = 5
BC = √((3-4)^2 + (5-3)^2) = √(1+4) = √5
CD = √((-1-3)^2 + (2-5)^2) = √(16+9) = √25 = 5
DA = √((0+1)^2 + (0-2)^2) = √(1+4) = √5
Step 2: Calculate the slopes of the sides
The slope of a line passing through two points (x1, y1) and (x2, y2) is given by (y2-y1)/(x2-x1).
Using this formula, we can find the slopes of each side:
mAB = (3-0)/(4-0) = 3/4
mBC = (5-3)/(3-4) = 2/-1 = -2
mCD = (2-5)/(-1-3) = -3/-4 = 3/4
mDA = (0-2)/(0+1) = -2/1 = -2
Step 3: Analyze the properties of the sides and angles
1. Opposite sides are equal in length:
AB = CD = 5
2. Opposite sides are parallel:
The slopes of AB and CD are equal (3/4), and the slopes of BC and DA are equal (-2).
3. Opposite angles are equal:
Angle A and angle C are opposite angles, and they are equal.
Conclusion:
Based on the above analysis, the quadrilateral formed by the given vertices is a parallelogram.
A = (0, 0)
B = (4, 3)
C = (3, 5)
D = (-1, 2)
To determine the type of quadrilateral formed by these vertices, we need to analyze the properties of the sides and angles.
Step 1: Calculate the lengths of the sides
Using the distance formula, we can find the length of each side of the quadrilateral:
AB = √((4-0)^2 + (3-0)^2) = √(16+9) = √25 = 5
BC = √((3-4)^2 + (5-3)^2) = √(1+4) = √5
CD = √((-1-3)^2 + (2-5)^2) = √(16+9) = √25 = 5
DA = √((0+1)^2 + (0-2)^2) = √(1+4) = √5
Step 2: Calculate the slopes of the sides
The slope of a line passing through two points (x1, y1) and (x2, y2) is given by (y2-y1)/(x2-x1).
Using this formula, we can find the slopes of each side:
mAB = (3-0)/(4-0) = 3/4
mBC = (5-3)/(3-4) = 2/-1 = -2
mCD = (2-5)/(-1-3) = -3/-4 = 3/4
mDA = (0-2)/(0+1) = -2/1 = -2
Step 3: Analyze the properties of the sides and angles
1. Opposite sides are equal in length:
AB = CD = 5
2. Opposite sides are parallel:
The slopes of AB and CD are equal (3/4), and the slopes of BC and DA are equal (-2).
3. Opposite angles are equal:
Angle A and angle C are opposite angles, and they are equal.
Conclusion:
Based on the above analysis, the quadrilateral formed by the given vertices is a parallelogram.
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Community Answer
What kind of a quadrilateral is formed by the vertices (0, 0), (4, 3),...
Let the points be A(0, 0), B(4, 3), C(3, 5) and D(-1, 2)
Let A and B be the easy points then,
The sides are equal. So, the quadrilateral is at least a parallelogram.
and (AC)2 ≠ (AB)2 + (BC)2
Therefore, the quadrilateral is not rectangle.
So, the given quadrilateral is a parallelogram.
Let A and B be the easy points then,
The sides are equal. So, the quadrilateral is at least a parallelogram.
and (AC)2 ≠ (AB)2 + (BC)2
Therefore, the quadrilateral is not rectangle.
So, the given quadrilateral is a parallelogram.
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