Question

6) If the four points (0, -1) (6, 7) (-2, 3) and (8,3) are
the vertices of a rectangle, then its area
a)40 sq. units
b) 20 sq. units
c) 100 sq. units
d) None​

Answer 1

option (d)

Step-by-step explanation:

Given :-

The four points (0, -1) (6, 7) (-2, 3) and (8,3) are

the vertices of a rectangle.

To find :-

Find its area?

Solution :-

Given vertices of a rectangle are (0, -1) (6, 7) (-2, 3) and (8,3)

Let A(0,-1) , B(6,7) , C(-2,3) and D(8,3)

We know that

Opposite sides are equal in a rectangle

On taking the vertices in the order then

=> AB = CD and BC = AD

Now,

We know that

The distance between two points (x1, y1) and

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

Finding AB :-

Let (x1, y1) = A(0,-1) => x1 = 0 and y1 = -1

Let (x2, y2) = B(6,7) => x2 = 6 and y2 = 7

AB = √[(6-0)²+(7-(-1))²]

=> AB = √(6²+(7+1)²)

=> AB = √(36+8²)

=> AB = √(36+64)

=> AB = √100

=> AB = 10 units

=> CD = 10 units

Finding AD :-

Let (x1, y1) = A(0,-1) => x1 = 0 and y1 = -1

Let (x2, y2) = D(8,3) => x2 = 8 and y2 = 3

AD = √[(8-0)²+(3-(-1))²]

=> AD = √(8²+(3+1)²)

=> AD = √(8²+4²)

=> AD = √(64+16)

=> AD = √80

=> AD = √(16×5)

=> AD = 4√5 units

=> BC = 4√5 units

We know that

Area of a rectangle = length×breadth sq.units

Area of the rectangle ABCD

=> AB×BC = AD×CD

=> 10×4√5 sq.units

=> 40√5 sq.units

Answer:-

Area of the given rectangle is 40√5 sq.units

Used formulae:-

→ The distance between two points (x1, y1) and

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

→ Area of a rectangle = length×breadth sq.units

→ Opposite sides are equal in a rectangle