The key is solving this problem is remembering the division of quadrants and how the sign of the x- and y-coordinates determines the quadrant. The picture diagram below helps greatly.

Using the diagram as a guide, we remember that a point is only in Quadrant II if the x-coordinate is negative while the y-coordinate is positive. We therefore need only to look at all of the points in our list to determine how many satisfy these conditions. Two of the points,and, both have x-coordinates that are negative. However, neither of these have positive y-coordinates. In, the y-coordinate is negative, which means the point is in Quadrant III. in, the y-coordinate is, meaning that the point lies on the x-axis rather than in any quadrant. Therefore, none of the listed points are in Quadrant II, meaning our answer is.

The point given in the problem is expressed as an ordered pair in the form. The number in the place of theis called the x-coordinate and tells how far from the origin to move horizontally, while the number in place of theis called the y-coordinate and tells how far to move from the origin vertically. The coorinate plane (the set of axes we graph points on) is divided into four regions (or quadrants) by the x-axis and y-axis. The top right region is Quadrant I, the top left region is Quadrant II, the bottom left region is Quadrant III, and the bottom right region is Quadrant IV.

Going back to our x-coordinate and y-coordinate, a postive x-coordinate means we move right from the origin the same number of units as the value. A negative x-coordinate means we move left from the origin. With y-coordinates, a positive value means we move up, while a negative value means we move down the indicated number of units. Since the ordered pair given in the problem is, our x-coordinate isand our y-coordinate is. That means we should move left from the origin five units and then down three units. The resulting plotted point is shown.

Having plotted the point we can clearly see that we are in Quadrant III, giving us the correct answer. In general, we can actually determine the quadrant of a point without plotting if we keep some general rules in mind. If the x- and y-coordinates are both positive, we are in Quadrant I. If the x-coordinate is negative while the y-coordinate remains positive, we are in Quadrant II. If both coordinates are negative, we are in Quadrant III. Finally, if the x-coordinate is positive while the y-coordinate is negative, we are in Quadrant IV. If either of the coordinates happens to be zero, our point will lie on one of the axes.

Substituteforand 8 for, and solve for:

For each of the five choices, substitute the coordinates forandin that order, and test the validity of the resulting equation. Below is the proof thatis on the graph:

:

这是真的,is on the graph.

The points,, andcan all be proved by the same procedure to be part of the graph.

However, we can prove thatis not on the graph by the same procedure:

This is false, sois proved to be not on the graph. This is the correct choice.

Substitute 10 forandfor, and then solve for:

By definition, a point on the coordinate plane that is in Quadrant III must have both a negativecoordinate and a negativecoordinate. The only answer choice that satisfies both of these conditions is.

The pointhas a negativecoordinate and a positivecoordinate. By definition, any point on a coordinate plane with these characteristics is located in Quadrant II.

The pointdoes not move in any direction on the-axis, but does moveunits up on the-axis. Therefore, the point is located only on the-axis.

By definition, a point with a negative-coordinate and a negative-coordinate lies in Quadrant III on the coordinate plane.

All points in Quadrant II have negative-coordinates and positive-coordinates. The only answer that fulfills these criteria is.