Problem 51 - Algebra 1

Question

Plot the ordered pairs in a coordinate plane. $$(-1,-2),(-4,5),(0,2)$$

Step-by-Step Solution

Answer

The points (-1,-2), (-4,5) and (0,2) have been successfully plotted on the coordinate plane.

Step 1: Understand Co-ordinate Plane and Ordered Pairs

A coordinate plane is essentially a two-dimensional number line where the horizontal line is x-axis and the vertical line is y-axis. An ordered pair is a pair of two things where one has a defined first and last term. Here, each ordered pair represents two coordinates: the x (horizontal) and y (vertical) coordinates on a plane.

Step 2: Plot the First Point (-1, -2)

Start at the origin (where the x and y axis intersect). Move 1 unit to the left as x-coordinate is -1. Now move 2 units downward as y-coordinate is -2. Mark this point as (-1,-2).

Step 3: Plot the Second Point (-4, 5)

Again, starting from the origin, move 4 units to the left (since the x-coordinate is -4) and 5 units upward (since the y-coordinate is 5). Mark this point as (-4,5).

Step 4: Plot the Third Point (0, 2)

From the origin, there is no need to move left or right as the x-coordinate in this pair is 0. Move 2 units upward because the y-coordinate is 2. Mark this point as (0,2).

Key Concepts

Ordered Pairs

Ordered pairs are fundamental in understanding the coordinate plane. An ordered pair consists of two elements enclosed in parentheses, such as \((-1, -2)\). The first element corresponds to the x-coordinate, and the second element corresponds to the y-coordinate. This order is crucial because it determines the precise position of a point on the coordinate plane.

Consider the ordered pair \((-1, -2)\). Here, \(-1\) represents the value along the x-axis, while \(-2\) specifies the value along the y-axis. By understanding these values, you can accurately place the point on the coordinate plane. When plotting, always start from the origin \((0,0)\), which is the center point where the x-axis and y-axis intersect.

A helpful hint: when reading ordered pairs, always pay attention to the order. This ensures you move correctly along the x and y directions.

X-axis

The x-axis is a crucial reference line on the coordinate plane. It's the horizontal line that spans left and right, acting as a guide for plotting ordered pairs. Every point along the x-axis has a y-coordinate of zero.

Imagine the x-axis as a number line extending horizontally across the plane. Positive values appear to the right of the origin \((0,0)\), while negative values extend to the left.

• When plotting points, the x-coordinate tells you how far to move horizontally from the origin. For instance, in the point \((-1, -2)\), you would move 1 unit to the left because the x-coordinate is \(-1\).
• If a point has an x-coordinate of 0, it means there is no horizontal movement, and the point lies directly above or below the origin on the y-axis.

Understanding the role of the x-axis helps in accurately plotting and reading ordered pairs.

Y-axis

The y-axis complements the x-axis and is the vertical line on the coordinate plane. It acts as a guide for determining the up and down position of points defined by the ordered pairs. Points on the y-axis have an x-coordinate of zero.

Think of the y-axis as a vertical number line from which you measure off movement upwards and downwards. Positive y-values are above the origin while negative y-values sit below it.

• When plotting, the y-coordinate tells you how far to move vertically from the x-axis. For example, for the point \((-1, -2)\), after moving left one unit for the x-coordinate, you move two units downwards because the y-coordinate is \(-2\).
• Points with a y-coordinate of zero lie directly on the x-axis, without requiring any vertical movement, such as at point \((3, 0)\).

Grasping how to navigate the y-axis is vital for correctly situating points on the coordinate plane.