Ordered Pairs
Ordered Pairs introduces the coordinate system notation where a point is represented as (x, y) with the horizontal coordinate listed first and the vertical coordinate second. Covered in Yoshiwara Elementary Algebra Chapter 1: Variables, this fundamental concept helps Grade 6 students precisely identify and plot points on the coordinate plane. The order of coordinates matters: (3, 5) and (5, 3) are different points.
Key Concepts
Property We write the coordinates of point inside parentheses as an ordered pair . The order of the coordinates makes a difference. We always list the horizontal coordinate first, then the vertical coordinate.
Examples The ordered pair $(5, 8)$ represents a point that is 5 units along the horizontal axis and 8 units along the vertical axis. To plot the point $(2, 9)$, you start at the origin, move 2 units horizontally, and then 9 units vertically. The point with coordinates $(0, 6)$ is located on the vertical axis, 6 units up from the origin.
Explanation An ordered pair is like an address for a point on a graph. The first number tells you how far to move along the horizontal axis, and the second number tells you how far to move up or down the vertical axis.
Common Questions
What is an ordered pair?
An ordered pair is a pair of numbers (x, y) used to identify a point on the coordinate plane. The first number is the horizontal position (x-axis) and the second is the vertical position (y-axis).
Why does the order matter in an ordered pair?
Because (x, y) and (y, x) represent different points unless x = y. The horizontal coordinate always comes first.
How do you plot an ordered pair on a graph?
Start at the origin (0, 0), move right or left by the x-value, then up or down by the y-value to find the point.
Where are ordered pairs covered in Yoshiwara Elementary Algebra?
Ordered pairs are introduced in Chapter 1: Variables of Yoshiwara Elementary Algebra.
What does a negative value in an ordered pair mean?
A negative x-value means moving left from the origin; a negative y-value means moving down. For example, (-3, 2) is 3 left and 2 up.