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](https://tex.z-dn.net/?f=%5Csqrt%7B%280-0%29%5E2%2B%280-b%29%5E2%7D%5C%5C%5C%5C%3D%5Csqrt%7Bb%5E2%7D%5C%5C%5C%5C%3Db%5C%20units)
Similarly,
Distance between CD is given by
![\sqrt{(a-a)^2+(0-b)^2}\\\\=\sqrt{b^2}\\\\=b\ units](https://tex.z-dn.net/?f=%5Csqrt%7B%28a-a%29%5E2%2B%280-b%29%5E2%7D%5C%5C%5C%5C%3D%5Csqrt%7Bb%5E2%7D%5C%5C%5C%5C%3Db%5C%20units)
On the other hand,
Distance between BC is given by
![\sqrt{(a-0)^2+(b-b)^2}\\\\=\sqrt{a^2}\\\\=a\ units](https://tex.z-dn.net/?f=%5Csqrt%7B%28a-0%29%5E2%2B%28b-b%29%5E2%7D%5C%5C%5C%5C%3D%5Csqrt%7Ba%5E2%7D%5C%5C%5C%5C%3Da%5C%20units)
Distance between AD is given by
![\sqrt{(0-a)^2+(0-0)^2}\\\\=\sqrt{a^2}\\\\=a\ units](https://tex.z-dn.net/?f=%5Csqrt%7B%280-a%29%5E2%2B%280-0%29%5E2%7D%5C%5C%5C%5C%3D%5Csqrt%7Ba%5E2%7D%5C%5C%5C%5C%3Da%5C%20units)
Since the lengths of opposite sides are equal,
So, it satisfies the property of rectangle.
Hence, Option 'B' is correct.