Find the perimeter of rectangle QRST, whose vertices are

Question

Q(–2, 2), R(1, 0), S(0, –1), and T(–3, 1)?

A. 

5.02 units 
B. 
5.09 units 
C. 
7.29 units 
D. 
10.04 units

Answer 1

The vertices of the rectangle are Q(–2, 2), R(1, 0), S(0, –1), and T(–3, 1).

Formula : Distance between two points (x₁, y₁) and (x₂, y₂) :

d = √[(x₂ - x₁)² + (y₂ - y₁)²].

 

Q = (x₁, y₁) = (-2, 2) and R = (x₂, y₂) = (1, 0)

QR = √[{(1 - (-2)}² + {0 - 2}²] = √[(3)² + (- 2)²] = √13

 

R = (x₁, y₁) = (1, 0) and S = (x₂, y₂) = (0, -1)

RS = √[{0 - (-1)}² + {(-1) - 0}²] = √[1+1] = √2

 

For any rectangle opposite sides are equal.

So QR = ST = √13.

RS = TQ = √2.

 

Perimeter of the rectangle = QR + RS + ST + TQ= √13 + √2 + √13 + √2

= 2( √13 + √2 )

= 2 ( 3.61 + 1.41 )

= 2 ( 5.02 )

= 10.04 units.

Solution : Perimeter of the rectangle is 10.04 units.