Answer: The correct option is (d) 35 units².
Step-by-step explanation: We are given to find the area of a rectangle with vertices at the points (2, 3), (7, 3), (7, 10), and (2, 10).
Let A(2, 3), B(7, 3), C(7, 10), and D(2, 10) represents the co-ordinates of the vertices of the given rectangle.
Then, the lengths of the sides AB, BC, CD and DA ca be calculated using distance formula as follows :
![AB=\sqrt{(7-2)^2+(3-3)^2}=\sqrt{25+0}=\sqrt{25}=5~\textup{units},\\\\BC=\sqrt{(7-7)^2+(10-3)^2}=\sqrt{0+49}=\sqrt{49}=7~\textup{units},\\\\CD=\sqrt{(2-7)^2+(10-10)^2}=\sqrt{25+0}=\sqrt{25}=5~\textup{units},\\\\DA=\sqrt{(2-2)^2+(3-10)^2}=\sqrt{0+49}=\sqrt{49}=7~\textup{units}.](https://tex.z-dn.net/?f=AB%3D%5Csqrt%7B%287-2%29%5E2%2B%283-3%29%5E2%7D%3D%5Csqrt%7B25%2B0%7D%3D%5Csqrt%7B25%7D%3D5~%5Ctextup%7Bunits%7D%2C%5C%5C%5C%5CBC%3D%5Csqrt%7B%287-7%29%5E2%2B%2810-3%29%5E2%7D%3D%5Csqrt%7B0%2B49%7D%3D%5Csqrt%7B49%7D%3D7~%5Ctextup%7Bunits%7D%2C%5C%5C%5C%5CCD%3D%5Csqrt%7B%282-7%29%5E2%2B%2810-10%29%5E2%7D%3D%5Csqrt%7B25%2B0%7D%3D%5Csqrt%7B25%7D%3D5~%5Ctextup%7Bunits%7D%2C%5C%5C%5C%5CDA%3D%5Csqrt%7B%282-2%29%5E2%2B%283-10%29%5E2%7D%3D%5Csqrt%7B0%2B49%7D%3D%5Csqrt%7B49%7D%3D7~%5Ctextup%7Bunits%7D.)
So, the area of the given rectangle will be
![Area=AB\timesBC=5\times7=35~\textup{units}^2.](https://tex.z-dn.net/?f=Area%3DAB%5CtimesBC%3D5%5Ctimes7%3D35~%5Ctextup%7Bunits%7D%5E2.)
Thus, (d) is the correct option.