Question

. Draw a rectangle ABCD (graph paper) whose vertices are A(3, 1) , B( "-5," 1) C(-5,-3) and D(3, "-3)." Also find the perimeter and area of the rectangle.​

Answer 1

Answer:

From the graph,

The coordinates of point D are (3,3).

Area of rectangle ABCD=l×b=AB×BC

On further calculation we get

Area of rectangle ABCD=6×2

Area of rectangle ABCD=12 sq. units

Answer 2

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A(3,1), B(-5,1), C(-5,3) D(3, "-3).

Let say D = (x , y)

AD = BC

=> √(x - 3)² +(y - 1)² = √(-3 + 3)² + ( 1 - 3)²

=> (x - 3)² +(y - 1)² = 4

=> x² + y² - 6x - 2y = -6

CD = AB

=> √(x +3)² +(y -3)² = √(-3 - 3)² + (1 - 1)²

=> (x +3)² +(y - 3)² = 36

=> x² + y² + 6x -6 y = 18

=> 12x - 4y = 24

=> 3x - y = 6

BD=AC

=> (x +3)² +(y -1)² = 36 + 4

(x +3)² +(y - 3)² = 36

=>(y - 1)² - (y - 3)² = 4

=> 4y - 8 = 4

=> y =3

3x - y = 6

=> 3x =9

=> x = 3