Answer:
The coordinates of O is (d,c) .
Option (a) is correct .
Step-by-step explanation:
As given
In the coordinate plane, three vertices of rectangle MNOP are M(0, 0), N(0, c), and P(d, 0).
As MNOP is a rectangle .
Thus opposite sides of the rectangles are equal .
Formula
\(Distance\ formula = \sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2} }\)
\(NM = \sqrt{(0-0)^{2}+(c-0)^{2}}\)
\(NM = \sqrt{c^{2}}\)
NM = c units
\(MP = \sqrt{(d-0)^{2}+(0-0)^{2}}\)
\(MP = \sqrt{d^{2}}\)
MP = d units
Thus the coordinate of the O (d,c) .
(This is because opposit sides of the rectangle are equal thus distance of point O from point P must be d and distance of point O from point N must be c .)
Therefore the coordinates of O is (d,c) .
Option (a) is correct .
