Question

What is the perimeter of the rectangle shown on the coordinate plane, to the nearest tenth of a unit?

Answer 1

Answer:

Perimeter of rectangle = 6√26 or 30.59 units

Step-by-step explanation:

Let the rectangle ABCD

so, co-ordinate of A= (-6,4) = (x1,y1)

co-ordinate of B= (4,2) = (x2,y2)

co-ordinate of C= (3,-3) = (x3,y3)

co-ordinate of D= (-7,-1) = (x4,y4)

In rectangle ABCD

AB = CD ( opposite sides of rectangle are equal)

and, AD = BC ( opposite sides of rectangle are equal)

Now, using distance formula

AB = √(x2-x1)² + (y2-y1)²

     =√(4-(-6))²+ (2-4)²

     =√(4+6)² + (-2)²

     =√(10)² + (4)

      =√100+4

      =√104

      =2√26 units

so,AB = CD = 2√26 units

again,by using distance formula

     BC = √(x3-x2)² + (y3-y2)²

           =√(3-4)² + ( -3-2)²

           =√(-1)² + (-5)²

           =√1 + 25

           =√26 units

so, AD = BC =√26 units

Now,

  Perimeter of rectangle = 2(length of rectangle+breadth of rectangle)

    =2(2√26 + √26)           (AB =CD = 2√26 units & AD = BC = √26 units)

    =2.3√26

     =6√26 units

Answer is 6√26 or 30.59 units