Two numbers make a place
One number is not enough on a floor.
Shalini's pin
Reiaan cannot see the room. His sister Shalini makes a map of the floor with pins and wool so he can feel where things are. She wants to tell him exactly where one pin is, using only numbers.
How many numbers does she need to name the exact place of a pin on the floor?
What this lesson covers
The idea
A coordinate system uses numbers to describe the exact location of points; the 2-D system uses two lines at right angles: the horizontal x-axis and the vertical y-axis.
Shalini's pin
Reiaan cannot see the room. His sister Shalini makes a map of the floor with pins and wool so he can feel where things are. She wants to tell him exactly where one pin is, using only numbers.
How many numbers does she need to name the exact place of a pin on the floor?
- 1 number
- 2 numbers
- 3 numbers
Find the pin
Each square of the floor is 1 foot. Follow Shalini's clues, one at a time.
Two numbers, two lines
A coordinate system uses numbers to describe the exact location of points. The 2-D system uses two lines at right angles: the horizontal x-axis and the vertical y-axis.
One number told you only a line of places. The second number, from the other line, cut it down to one point.
Notes
Two numbers fix a point on a plane. The 2-D coordinate system uses two lines at right angles: the horizontal x-axis and the vertical y-axis.
Check yourself
Shalini says: "The pin is 4 feet from the left wall." Can Reiaan find the pin from this clue alone?
In the 2-D coordinate system, which two lines do we use?
The horizontal line of the coordinate system is called the…
Two clues: "6 feet from the left wall" and "3 feet up from the bottom wall". How many places on the floor fit both clues?
Answer: 1
Each clue gives a line of places. The two lines cross at exactly one point, so only one place fits both.
- Yes, there is only one place 4 feet from the left wall.. No. Every place on the line 4 feet from the left wall fits. That is a whole line of places.
- Not yet. He needs one more number. — correct. Right. A second number, the distance up from the bottom wall, picks one place on that line.
- Not yet. He needs two more numbers.. One more is enough. Two numbers in all fix a place on a floor.
- Two lines at right angles: one horizontal, one vertical — correct. Yes: the horizontal x-axis and the vertical y-axis.
- Two lines running side by side (parallel). The two axes cross at right angles. Parallel lines do not cross.
- One long line only. One line gives only one number, and that fixes just a line of places, as with one clue on the floor.
- x-axis — correct. Yes. The x-axis is the horizontal line.
- y-axis. The y-axis is the vertical line, the one that goes up and down.