Coordinate points are given x-coordinate first, y-coordinate second.  The correct representation plots the point one unit to the left of the origin on the x-axis and four units up from the origin on the y-axis.

Coordinate points are given x-coordinate first, y-coordinate second.

(-2, 1), (2, 4) is correct because it list the coordinates of each point in the correct order.

(1, -2), (4, 2) is incorrect because it lists the coordinates of each point in the incorrect order.

(2, 4), (-2, 1) is incorrect because, while it lists the coordinates of each point correctly, it misidentifies the points.

(4, 2), (1, -2) is incorrect because it both lists the coordinates of each point in the incorrect order and misidentifies the points.

If \(\displaystyle A\) and \(\displaystyle B\) have the same sign, then \(\displaystyle AB > 0\), and the point has a positive \(\displaystyle x\)-coordinate. The sign of \(\displaystyle A + B\) is the same as the common sign of \(\displaystyle A\) and \(\displaystyle B\). Therefore, only the \(\displaystyle x\)-coordinate restricts the possibilities.

The points witn positive \(\displaystyle x\)-coordinates are in Quadrant I and Quadrant IV.

The ordered pair \(\displaystyle (4,3)\) consists of a positive \(\displaystyle x\)-coordinate and a positive \(\displaystyle y\)-coordinate. The only quadrant that consists entirely of positive \(\displaystyle x\)- and \(\displaystyle y\)-coordinates is Quadrant I. 

The ordered pair \(\displaystyle (5,0)\) consists of a positive \(\displaystyle x\)-coordinate and a \(\displaystyle y\)-coordinate of \(\displaystyle 0\). The only part of the coordinate plane on which all points have a zero \(\displaystyle y\)-coordinate is the \(\displaystyle x\)-axis. 

By definition, only Quadrant III contains ordered pairs that have both negative \(\displaystyle x\)- and \(\displaystyle y\)-coordinates. 

The ordered pair \(\displaystyle (-1,3)\) has a negative \(\displaystyle x\)-coordinate and a positive \(\displaystyle y\)-coordinate. By definition, all ordered pairs with negative \(\displaystyle x\)-coordinates and a positive \(\displaystyle y\)-coordinates exist in Quadrant II.

The ordered pair \(\displaystyle (0,7)\) has a zero \(\displaystyle x\)-coordinate and a nonzero \(\displaystyle y\)-coordinate. By definition, all ordered pairs with zero \(\displaystyle x\)-coordinates and nonzero \(\displaystyle y\)-coordinates is on the \(\displaystyle y\)-axis.

 By definition, all ordered pairs with positive \(\displaystyle x\)-coordinates and positive \(\displaystyle y\)-coordinates are in Quadrant I. Therefore, the only ordered pair in this quadrant is \(\displaystyle (2,7)\).

The quadrants are numbered as follows:

The point (-2,3) has a negative x coordinate, so the point is on the left side of the y-axis, and a positive y-coordinate, so the point is above the x-axis.

That places it in quadrant II.