Question

Which ordered pair locates point P on the coordinate plane?

Point P on a coordinate plane, located 3 units to the left of the vertical axis and 2 units below the horizontal axis.
A. (–3, –2)
B. (–3, 2)
C. (–2, –3)
D. (–3, –3)

Answer 1

Answer:

The coordinate plane was developed centuries ago and refined by the French mathematician René Descartes. In his honor, the system is sometimes called the Cartesian coordinate system. The coordinate plane can be used to plot points and graph lines. This system allows us to describe algebraic relationships in a visual sense, and also helps us create and interpret algebraic concepts.

Getting to Know the Coordinate Plane

You have likely used a coordinate plane before. For example, have you ever used a gridded overlay to map the position of an object? (This is often done with road maps, too.)

This “map” uses a horizontal and vertical grid to convey information about an object’s location. Notice that the letters A-F are listed along the top, and the numbers 1-6 are listed along the left edge. The general location of any item on this map can be found by using the letter and number of its grid square. For example, you can find the item that exists at square “4F” by moving your finger along the horizontal to letter F and then straight down so you are in line with the 4. You’ll find a blue disc is at this location on the map.

The coordinate plane has similar elements to the grid shown above. It consists of a horizontal axis and a vertical axis, number lines that intersect at right angles. (They are perpendicular to each other.)

The horizontal axis in the coordinate plane is called the x-axis. The vertical axis is called the y-axis. The point at which the two axes intersect is called the origin. The origin is at 0 on the x-axis and 0 on the y-axis.

The intersecting x- and y-axes divide the coordinate plane into four sections. These four sections are called quadrants. Quadrants are named using the Roman numerals I, II, III, and IV beginning with the top right quadrant and moving counter clockwise.

Locations on the coordinate plane are described as ordered pairs. An ordered pair tells you the location of a point by relating the point’s location along the x-axis (the first value of the ordered pair) and along the y-axis (the second value of the ordered pair).

In an ordered pair, such as (x, y), the first value is called the x-coordinate and the second value is the y-coordinate. Note that the x-coordinate is listed before the y-coordinate. Since the origin has an x-coordinate of 0 and a y-coordinate of 0, its ordered pair is written (0, 0).

Answer 2

Given:

Point P located 3 units to the left of the vertical axis and 2 units below the horizontal axis on a coordinate plane.

To find:

Ordered pair of coordinates of point P on the coordinate plane.

Solution:

The coordinates plane consists of vertical and horizontal axes. The vertical axis is the $y-$axis and the horizontal axis is the $x-$axis. Both these axes meet at origin (0,0), i.e., when $x=0$ and $y=0$. A point is located on the coordinate plane through the ordered pair $(x,y)$. Upper and lower areas of the vertical axis from origin are positive and negative halves of $y-$axis. Right and left areas of the horizontal axis from origin are positive and negative halves of $x-$axis.

Left of the verical axis indicates negative half of $x-$axis.

Below horizontal axis indicates negative half of $y-$axis.

3 units left to negative half of $x-$axis is $x=-3$

2 units below negative half of $y-$axis is $y=-2$

The ordered pair of $P(x,y)$ is determined as to be $P(-3,-2)$ from the above information. Thus, option (A) is correct.

Option (B) is incorrect because though its $x-$coordinate is correct, its $y-$coordinate is in positive half of $y-$axis which is incorrect.

Option (C) is incorrect because the coordinates are in reverse order as from what is asked in the problem.

Option (D) is incorrect because $y-$coordinate is incorrect as the problem says it is 2 units below horizontal and not 3 units.

Point P on a coordinate plane, located 3 units to the left of the vertical axis and 2 units below the horizontal axis is P(-3,-2). The correct option is Option (A).