Question

45. Name the type of quadrilateral formed by the points (0,0), (0, 1), (1, 1), (1,0) and give reasons for your answers.​

Answer 1

Given :-

The points (0,0), (0, 1), (1, 1), (1,0)

To find :-

The quadrilateral formed by the given points.

Solution :-

Given points are (0,0), (0, 1), (1, 1), (1,0)

Let A = (0,0)

Let B = (0, 1)

Let C = (1, 1)

Let D = (1,0)

We know that

The distance between two points (x1, y1) and (x2, y2) is √[(x2-x1)²+(y2-y1)²] units

Length of AB :-

Let (x1, y1) = A(0,0) => x1 = 0 and y1 = 0

Let (x2, y2) = B(0,1) => x2 = 0 and y2 = 1

By distance formula

AB = √[(0-0)²+(1-0)²]

=> AB = √(0²+1²)

=> AB = √(0+1)

=> AB = √1

Therefore, AB = 1 unit

Length of BC :-

Let (x1, y1) = B(0,1) => x1 = 0 and y1 = 1

Let (x2, y2) = C(1,1) => x2 = 1 and y2 = 1

By distance formula

BC = √[(1-0)²+(1-1)²]

=> BC = √(1²+0²)

=> BC = √(1+0)

=> BC = √1

Therefore, BC = 1 unit

Length of CD :-

Let (x1, y1) = C(1,1) => x1 = 1 and y1 = 1

Let (x2, y2) = D(1,0) => x2 = 1 and y2 = 0

By distance formula

CD = √[(1-1)²+(0-1)²]

=> CD = √(0²+(-1²))

=> CD = √(0+1)

=> CD= √1

Therefore, CD = 1 unit

Length of AD :-

Let (x1, y1) = A(0,0) => x1 = 0 and y1 = 0

Let (x2, y2) = D(1,0)=> x2 = 1 and y2 = 0

By distance formula

AD = √[(1-0)²+(0-0)²]

=> AD = √(1²+0²)

=> AD = √(1+0)

=> AD = √1

Therefore, AD = 1 unit

Length of AC :-

Let (x1, y1) = A(0,0) => x1 = 0 and y1 = 0

Let (x2, y2) = C(1,1) => x2 = 1 and y2 = 1

By distance formula

AC = √[(1-0)²+(0-1)²]

=> AC = √[1²+(-1²)]

=> AC = √(1+1)

=> AC = √2

Therefore, AC = √2 units

Length of BD :-

Let (x1, y1) = B(0,1) => x1 = 0 and y1 = 1

Let (x2, y2) = D(1,0) => x2 = 1 and y2 = 0

By distance formula

BD = √[(1-0)²+(1-0)²]

=> BD = √(1²+1²)

=> BD = √(1+1)

=> BD = √2

Therefore, BD= √2 units

We have,

AB = 1 unit

BC = 1 unit

CD = 1 unit

AD = 1 unit

AC = √2 units

BD = √2 units

Name of the quadrilateral :-

The quadrilateral is a square .

Reason :-

We notice that

AB = BC = CD = AD and AC = BD

The lengths of the all sides are equal and the lengths of the diagonals are equal.

So, It is a square.

Answer :-

The quadrilateral formed by the given points is a Square.

Used formulae:-

Distance Formula:-

→The distance between two points

(x1, y1) and (x2, y2) is √[(x2-x1)²+(y2-y1)²] units

→ All sides are equal and Diagonals are equal in a square.

Answer 2

Step-by-step explanation:

Given :-

The points (0,0), (0, 1), (1, 1), (1,0)

To find :-

The quadrilateral formed by the given points.

Solution :-

Given points are (0,0), (0, 1), (1, 1), (1,0)

Let A = (0,0)

Let B = (0, 1)

Let C = (1, 1)

Let D = (1,0)

We know that

The distance between two points (x1, y1) and (x2, y2) is √[(x2-x1)²+(y2-y1)²] units

Length of AB :-

Let (x1, y1) = A(0,0) => x1 = 0 and y1 = 0

Let (x2, y2) = B(0,1) => x2 = 0 and y2 = 1

By distance formula

AB = √[(0-0)²+(1-0)²]

=> AB = √(0²+1²)

=> AB = √(0+1)

=> AB = √1

Therefore, AB = 1 unit

Length of BC :-

Let (x1, y1) = B(0,1) => x1 = 0 and y1 = 1

Let (x2, y2) = C(1,1) => x2 = 1 and y2 = 1

By distance formula

BC = √[(1-0)²+(1-1)²]

=> BC = √(1²+0²)

=> BC = √(1+0)

=> BC = √1

Therefore, BC = 1 unit

Length of CD :-

Let (x1, y1) = C(1,1) => x1 = 1 and y1 = 1

Let (x2, y2) = D(1,0) => x2 = 1 and y2 = 0

By distance formula

CD = √[(1-1)²+(0-1)²]

=> CD = √(0²+(-1²))

=> CD = √(0+1)

=> CD= √1

Therefore, CD = 1 unit

Length of AD :-

Let (x1, y1) = A(0,0) => x1 = 0 and y1 = 0

Let (x2, y2) = D(1,0)=> x2 = 1 and y2 = 0

By distance formula

AD = √[(1-0)²+(0-0)²]

=> AD = √(1²+0²)

=> AD = √(1+0)

=> AD = √1

Therefore, AD = 1 unit

Length of AC :-

Let (x1, y1) = A(0,0) => x1 = 0 and y1 = 0

Let (x2, y2) = C(1,1) => x2 = 1 and y2 = 1

By distance formula

AC = √[(1-0)²+(0-1)²]

=> AC = √[1²+(-1²)]

=> AC = √(1+1)

=> AC = √2

Therefore, AC = √2 units

Length of BD :-

Let (x1, y1) = B(0,1) => x1 = 0 and y1 = 1

Let (x2, y2) = D(1,0) => x2 = 1 and y2 = 0

By distance formula

BD = √[(1-0)²+(1-0)²]

=> BD = √(1²+1²)

=> BD = √(1+1)

=> BD = √2

Therefore, BD= √2 units

We have,

AB = 1 unit

BC = 1 unit

CD = 1 unit

AD = 1 unit

AC = √2 units

BD = √2 units

Name of the quadrilateral :-

The quadrilateral is a square .

Reason :-

We notice that

AB = BC = CD = AD and AC = BD

The lengths of the all sides are equal and the lengths of the diagonals are equal.

So, It is a square.

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