Class 10 Exam > Class 10 Questions > The points (1, 7), (4, 2), (– 1, 1) and...
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The points (1, 7), (4, 2), (– 1, 1) and (– 4, 4) are the vertices of a :
- a)parallelogram
- b)rhombus
- c)rectangle
- d)square.
Correct answer is option 'D'. Can you explain this answer?
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Verified Answer
The points (1, 7), (4, 2), (– 1, 1) and (– 4, 4) are the v...
Given points are (1,7),(4,2),(-1,-1),(-4,4)
Let the points are A,B,C,D.
Distance formula = √(x₂-x₁)^2+(y₂-y₁)^2
AB = √(4-1)^2+(2-7)^2
= √9+25
= √34
BC = √(-1-4)^2+(-1-2)^2
= √25+9
= √34
CD = √(-4-(-1))^2+(4-(-1))^2
= √9+25
= √34
DA = √(1-(-4))^2+(7-4)^2
= √25+9
= √34
We know that the all sides of the square are equal.
Here by the distance formula, we got the for sides equal .
So,from this we can say that these points are the vertices of a square.
Most Upvoted Answer
The points (1, 7), (4, 2), (– 1, 1) and (– 4, 4) are the v...
Vertices of a Square
The given points (1, 7), (4, 2), (-1, 1), and (-4, 4) can form the vertices of a square.
Properties of a Square
- A square is a special type of rectangle and rhombus.
- All sides of a square are equal in length.
- Opposite sides of a square are parallel.
- All angles in a square are right angles (90 degrees).
- The diagonals of a square are equal in length and bisect each other at right angles.
Verifying the Given Points
To verify if the given points form a square, we need to check the properties mentioned above.
- Calculate the distances between the points to ensure that all sides are equal.
- Check if the slopes of opposite sides are equal to show that they are parallel.
- Calculate the angles between the sides to confirm that they are all right angles.
- Calculate the lengths of the diagonals and check if they are equal.
Conclusion
After verifying the properties of the given points, if all conditions hold true, then the points (1, 7), (4, 2), (-1, 1), and (-4, 4) form the vertices of a square. Hence, the correct answer is option 'D' - square.
The given points (1, 7), (4, 2), (-1, 1), and (-4, 4) can form the vertices of a square.
Properties of a Square
- A square is a special type of rectangle and rhombus.
- All sides of a square are equal in length.
- Opposite sides of a square are parallel.
- All angles in a square are right angles (90 degrees).
- The diagonals of a square are equal in length and bisect each other at right angles.
Verifying the Given Points
To verify if the given points form a square, we need to check the properties mentioned above.
- Calculate the distances between the points to ensure that all sides are equal.
- Check if the slopes of opposite sides are equal to show that they are parallel.
- Calculate the angles between the sides to confirm that they are all right angles.
- Calculate the lengths of the diagonals and check if they are equal.
Conclusion
After verifying the properties of the given points, if all conditions hold true, then the points (1, 7), (4, 2), (-1, 1), and (-4, 4) form the vertices of a square. Hence, the correct answer is option 'D' - square.
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The points (1, 7), (4, 2), (– 1, 1) and (– 4, 4) are the vertices of a :a)parallelogramb)rhombusc)rectangled)square.Correct answer is option 'D'. Can you explain this answer?
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