Answer:
(a)The length of DA = 3.2 units (app.)
(b) The length of CD = 6.32 units
(c)Area of the rectangle = 20.2 sq units.
Step-by-step explanation:
Here the coordinates of the rectangle are given as
A(-3,0), B(3,2), C(4,-1) and D(-2,-3).
DISTANCE FORMULA: For two points P(a,b) and Q(c,d)
The length of PQ = [tex]\sqrt{(c-a)^2 + (d-b)^2}[/tex]
(a)The length of DA = [tex]\sqrt{(-3-0)^2+ (-2-(-3))^2} = \sqrt{(-3)^2+ (1)^2} \\= \sqrt{9+ 1} = \sqrt{10} = 3.16[/tex]
Hence, the length of DA = 3.2 units (app.)
(b) The length of CD = [tex]\sqrt{(-2-4)^2+ (-3-(-1))^2} = \sqrt{(-6)^2+ (-2)^2} \\= \sqrt{36+ 4} = \sqrt{40} = 7.28[/tex]
Hence, the length of CD = 6.32 units
(c)Now, area of the rectangle = LENGTH X WIDTH
= Length of DA x Length of CD
= 3.2 units x 6.32 units = 20.2 sq units.
