Question

Name the \(x\)-coordinate and \(y\)-coordinate of each ordered pair. \((5,8)\)

Short answer

x-coordinate: 5, y-coordinate: 8.

Step-by-step solution

Identifying the Ordered Pair

First, recognize that the ordered pair provided is \((5, 8)\). Ordered pairs are generally written in the form \((x, y)\), where the first element indicates the \(x\)-coordinate, and the second element indicates the \(y\)-coordinate.

Determining the x-coordinate

Examine the first number in the pair. For \((5, 8)\), the first number is 5. This number represents the \(x\)-coordinate, so we can say that the \(x\)-coordinate is 5.

Determining the y-coordinate

Examine the second number in the pair. For \((5, 8)\), the second number is 8. This number represents the \(y\)-coordinate, so we can say that the \(y\)-coordinate is 8.

Conclusion

To conclude, for the ordered pair \((5, 8)\), the \(x\)-coordinate is 5, and the \(y\)-coordinate is 8.

Key concepts

x-coordinate

Whenever you encounter an ordered pair, the first number in that pair is identified as the x-coordinate. This value tells us the position along the horizontal axis, or x-axis, of a coordinate system.
To visualize better, think of the x-axis as a line that runs left to right, like a horizon. The x-coordinate tells us how far to move right or left from the origin, which is the point \((0,0)\).

• If the x-coordinate is positive, move to the right of the origin.
• If it is negative, move to the left.

In the example of the ordered pair \((5,8)\), the first number is 5, indicating that to reach the correct position, you'll move 5 units to the right on the x-axis.

y-coordinate

The y-coordinate is equally important for locating a point in a coordinate system. It’s the second number in an ordered pair and shows how far to move along the vertical axis, or y-axis. Imagine a line running up and down like a pole. The y-coordinate guides you on how many units to climb up or down from the origin at \((0,0)\).

• If the y-coordinate is positive, move upwards from the origin.
• If it is negative, travel downwards.

For instance, in \((5,8)\), the y-coordinate is 8, meaning you need to move 8 units up on the y-axis. This movement shows the location above the x-axis.

ordered pair

An ordered pair is a crucial concept in understanding how to plot points in the coordinate plane. It consists of two values written in a specific order, \((x, y)\).
The order matters because it dictates which number corresponds to the x-coordinate and which to the y-coordinate. Without the correct order, the point could be incorrectly placed.

• The first element of the pair is always the x-coordinate, guiding horizontal movement.
• The second element is the y-coordinate, dictating vertical movement.

Together, these elements work as a precise set of instructions for finding any point on the plane. For example, in \((5,8)\), the first number 5 tells us how far to move horizontally, and the second number 8 tells us how far to go vertically. Combining these movements pinpoints the exact location of the point.