Question

Name the \(x\)-coordinate and \(y\)-coordinate of each ordered pair. \((11,0)\)

Short answer

The \(x\)-coordinate is 11 and the \(y\)-coordinate is 0.

Step-by-step solution

Identify the format

Ordered pairs are usually written in the format \((x, y)\), where the first value is the \(x\)-coordinate, and the second value is the \(y\)-coordinate.

Locate the x-coordinate

The first number in the ordered pair \((11, 0)\) is \(11\). This is the \(x\)-coordinate.

Locate the y-coordinate

The second number in the ordered pair \((11, 0)\) is \(0\). This is the \(y\)-coordinate.

Key concepts

coordinates

Coordinates are used in mathematics to uniquely determine the position of a point on a graph or a plane. Imagine a graph with two lines intersecting at right angles – these lines are your axes. Each point is specified by a pair of numbers known as ordered pairs, like \((x, y)\).

• The first number in the ordered pair is called the **x-coordinate**.
• The second number is referred to as the **y-coordinate**.

Coordinates essentially create a road map to the point they refer to on the graph. You can think of it like providing an address to find a friend's house. Without these coordinates, pinpointing the precise location would be challenging. Once you understand how to read these numbers, you'll easily find any spot on the graph!

Even though it might seem a bit abstract at first, visualizing it as a grid with streets and avenues might help. The x and y axes are your grid lines guiding you to the right spot.

x-coordinate

The x-coordinate is the first number in an ordered pair. It tells you how far to move horizontally on the graph from the origin, which is the point where the x and y axes meet. When you see the ordered pair \((11, 0)\), the x-coordinate means you move directly over to the right from the origin by 11 steps.

Understanding the Role of the x-coordinate

• If the x-coordinate is positive, the movement is to the right of the origin, towards positive x values.
• If it's negative, you'd move to the left, heading toward the negative side of the x-axis.

In our example, \((11, 0)\), the x-coordinate is 11, telling us exactly how far across on the horizontal line to place our point. Visualizing this will help solidify understanding – imagine standing at zero and counting 11 steps to plot the point.

y-coordinate

The y-coordinate, as the second number in an ordered pair, indicates how far to move vertically on the graph. In the ordered pair \((11, 0)\), the y-coordinate is 0, suggesting that there’s no movement up or down from the origin. You stay right at the level of the x-axis.

Interpreting the y-coordinate

• If the y-coordinate is positive, move upward on the graph from the x-axis.
• If it's negative, move downward toward the negative y values.

In simple terms, the y-coordinate shows how high or low your point should be compared to the starting line (x-axis). With the pair \((11, 0)\), since the y-coordinate is 0, it indicates no vertical change, keeping your point on the x-axis. Wrapping your head around ordered pairs by practicing will make this concept clearer and help in plotting points accurately.