Final Answer:
In this equation,2y = x, the ordinate 'y' is precisely twice the abscissa 'x,' satisfying the given geometric relationship. The option C is correct.
Step-by-step explanation:
The equation "The ordinate is twice the abscissa" is represented by option C) 2y = x. In this equation, 'x' represents the abscissa (horizontal coordinate) and 'y' represents the ordinate (vertical coordinate). The equation states that the ordinate (y) is equal to twice the abscissa (x). Therefore, option C) accurately captures the relationship described in the question.
Now, let's delve into the explanation. In the Cartesian coordinate system, any point can be represented as (x, y), where 'x' is the abscissa and 'y' is the ordinate. The given equation 2y = x implies that the ordinate 'y' is indeed twice the value of the abscissa 'x'. This relationship is consistent with the statement in the question, making option C) the correct representation.
To elaborate further, consider a numerical example. If we choose x = 3, then according to the equation 2y = x, we would have 2y = 3, and solving for 'y' would give y = 3/2. This confirms that for the chosen value of x, the ordinate y is indeed twice the abscissa, supporting the correctness of the equation 2y = x as the solution to the given geometric relationship. Therefore, option C) is the correct and precise representation of "The ordinate is twice the abscissa." Therefore option C is correct.