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.
