Question

If the coordinates of a quadrilateral composed in the first quadrant of the coordinate plane are (0,0), (0,b), (a,b), and (a,0), which is the most accurate classification of the quadrilateral?
A. trapezoid
B. Rectangle
C. Parallelogram
D. Square

Answer 1

Answer: Option 'B' is correct.

Step-by-step explanation:

Since we have given that the coordinates of a quadrilateral in the first quadrant of the coordinate plane are (0,0), (0,b), (a,b), and (a,0),

Distance between AB is given by

$\sqrt{(0-0)^2+(0-b)^2}\\\\=\sqrt{b^2}\\\\=b\ units$

Similarly,

Distance between CD is given by

$\sqrt{(a-a)^2+(0-b)^2}\\\\=\sqrt{b^2}\\\\=b\ units$

On the other hand,

Distance between BC is given by

$\sqrt{(a-0)^2+(b-b)^2}\\\\=\sqrt{a^2}\\\\=a\ units$

Distance between AD is given by

$\sqrt{(0-a)^2+(0-0)^2}\\\\=\sqrt{a^2}\\\\=a\ units$

Since the lengths of opposite sides are equal,

So, it satisfies the property of rectangle.

Hence, Option 'B' is correct.

Answer 2

I believe it is a Rectangle. So Answer B.