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Glacius
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Coordinates

A Cartesian ordered pair specifies horizontal and vertical coordinates relative to two perpendicular axes.

1 min read1 figureSources & further reading
On this page 7 sections
  1. Overview
  2. A flat map needs two numbers to locate a point
  3. Zero means no displacement on that axis
  4. Check your understanding
  5. Key takeaway
  6. Sources & further reading
  7. Concept connections

01A flat map needs two numbers to locate a point#

A flat map needs two numbers to locate a point. In (x,y)(x,y), xx gives horizontal position and yy gives vertical position. The axes meet at the origin, (0,0)(0,0).

For P=(3,2)P=(3,2), start at the origin: go 3 units right, then 2 units up. The first number belongs to the horizontal axis.

The horizontal x-axis and vertical y-axis meet at (0,0). Labeled integer ticks have equal spacing within each axis. Point P is at (3,2): three units right, two units up.The horizontal x-axis and vertical y-axis meet at (0,0). Labeled integer ticks have equal spacing within each axis. Point P is at (3,2): three units right, two units up.
Figure 1The horizontal x-axis and vertical y-axis meet at (0,0). Labeled integer ticks have equal spacing within each axis. Point P is at (3,2): three units right, two units up.
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Check your reasoning

Where is (−2,3)(-2,3) from the origin?

  1. ARight 2, down 3
  2. BLeft 2, up 3
  3. CLeft 3, up 2
Show answer and explanation
Left 2, up 3

The first coordinate is −2, so move left 2. The second is 3, so move up 3.

02Zero means no displacement on that axis#

Zero means no displacement on that axis. The point (0,−3)(0,-3) lies on the vertical axis, three units below the origin. A negative yy does not make xx negative.

Check your reasoning

A point is (0,−3)(0,-3). What is its vertical coordinate?

Show answer and explanation
-3

The vertical coordinate is the second entry, −3.

03Check your understanding#

Check your reasoning

On a map, east is positive x and north is positive y. A station is at (−4,1)(-4,1). How many units west of the origin is it?

Show answer and explanation
4

The horizontal coordinate −4 means four units west.

Key takeaway

Read x first, then y; each sign gives the direction from zero.

  • Locate a point from an ordered coordinate pair

Sources & further reading

  1. [1]

Reference this concept

Link to this page, a section, or an individual figure.

Glacius. “Coordinates.” Math behind ML. /learn/f-coordinates