Unit 6: Geometry · Lesson 10
Coordinate Plane Introduction
What this lesson is for
- Students will understand and practice Coordinate Plane Introduction
- Students will solve problems related to this topic
Wisdom is the principal thing; therefore get wisdom: and with all thy getting get understanding.
Proverbs 4:7
Coordinate Plane Introduction
The coordinate plane (also called the Cartesian plane) is a grid formed by two perpendicular number lines. It allows us to describe the exact location of any point using an ordered pair of numbers.
Key Terms:
- x-axis — the horizontal number line
- y-axis — the vertical number line
- Origin — the point where the axes cross; coordinates (0, 0)
- Ordered pair (x, y) — a pair of numbers giving the exact position of a point; x is horizontal, y is vertical
- Quadrant — one of the four regions of the coordinate plane
The Four Quadrants: | Quadrant | x-value | y-value | |----------|---------|---------| | I | positive (+) | positive (+) | | II | negative (−) | positive (+) | | III | negative (−) | negative (−) | | IV | positive (+) | negative (−) |
Reading an ordered pair: In (3, 5), start at the origin, move 3 units right (x = 3), then 5 units up (y = 5). Always go horizontal first, then vertical.
Example 1: `math Plot point A(4, 2): start at origin, move 4 right, 2 up → Quadrant I. Plot point B(−3, 1): move 3 left, 1 up → Quadrant II. `
Example 2: `math Name the quadrant for point (−2, −5). x is negative, y is negative → Quadrant III. `
René Descartes developed the coordinate system in the 1600s. By combining algebra and geometry, he changed mathematics forever. This is another example of how God gifted certain people with the ability to see hidden patterns in creation and develop tools that benefit all of humanity.
Guided practice
The horizontal number line on a coordinate plane is called the ___.
Show the steps and the answer
X comes before Y in the alphabet, and the x-axis is horizontal (left-right).
Answer: x-axis
What are the coordinates of the origin?
Show the steps and the answer
The origin is where the x-axis and y-axis meet, at zero on both.
Answer: (0, 0)
Point (3, 4) is in which quadrant?
Show the steps and the answer
Both coordinates are positive. Quadrant I is the upper right, where x and y are both positive.
Answer: I
Homework
Complete the practice problems for Coordinate Plane Introduction.
Note for the parent
Today's lesson covers Coordinate Plane Introduction. Estimated time: 40 minutes. Encourage independent work but be available for questions.
The first three of this lesson's 10 questions
The horizontal number line on the coordinate plane is called the:
Show the answer
Answer: x-axis
What are the coordinates of the origin?
Show the answer
Answer: (0, 0)
In the ordered pair (x, y), which value describes horizontal position?
Show the answer
Answer: x
Another 7 questions follow in the lesson itself, each one graded the moment it is answered.