Question

\((a, 6)\) is a point (not shown) in Quadrant I \((-6, b)\) is a point (not shown) in Quadrant II. $$\begin{array}{cc}\text { Quantity } \mathbf{A} & \text { Quantity } \mathbf{B} \\ a & b\end{array}$$ a. Quantity \(\mathrm{A}\) is greater. b. Quantity \(\mathrm{B}\) is greater. c. The two quantities are equal. d. The relationship cannot be determined from the information given.

Short answer

d. The relationship cannot be determined from the information given.

Step-by-step solution

Analyze the position of points in quadrants

In the Cartesian coordinate system, quadrant I is the section where both x and y coordinates are positive. Quadrant II, on the other hand, is the section where x is negative and y is positive. This means that \(a > 0\) and \(b > 0\). Here, it's also important to note that in both quadrants the points are given positive distances from the origin, which are 6 for point A and (-6) for point B.

Determine the possible signs of the variables

As (a, 6) is in quadrant I, then a is positive and greater than 0. Meanwhile, as (-6, b) is in quadrant II, b is also positive and greater than 0. The sign of a or b does not change the distance from the origin.

Compare the quantities of a and b

Since the absolute values of a and b would be equal to the respective distances from the origin for the given points, both a and b would be greater than 0 but less than or equal to 6. Thus we can conclude that the values of a and b are positive, but can't make any certain comparison about the magnitudes of a and b from the given information.