Fig. 1.4 · related Think and Reflect

Given:

S has signs (+, −); Q has signs (−, +).

To Find:

Their quadrants and the condition for swapped pairs to agree.

Property:

Ordered pairs agree only when corresponding entries agree.

Solution:

S lies in IV; Q lies in II.

On the y-axis x = 0; on the x-axis y = 0. Axis points have no quadrant.

For $\left(x,y\right)$ = $\left(y,x\right)$, comparison of the first entries gives x = y. Conversely, equal entries are unchanged by swapping.

Results:

The pairs coincide exactly when x = y.