17. Coordinate Plane Basics

Coordinate geometry turns points on a grid into lengths and relationships.

Key ideas:

• The \(x\)-coordinate moves left or right.
• The \(y\)-coordinate moves up or down.
• Horizontal distance is a change in \(x\).
• Vertical distance is a change in \(y\).

Example: from \((1,2)\) to \((5,2)\), only \(x\) changes. The distance is \(4\).

Common mistake: reversing the coordinates. \((3,5)\) and \((5,3)\) are different points.

Deepen your understanding
Use this focused guide to turn Coordinate Plane Basics into a dependable GED® problem-solving skill.

Learning targets

• Plot ordered pairs by moving in (x) first and (y) second.
• Identify axes, origin, quadrants, and the signs used in each quadrant.
• Find horizontal and vertical distances without a full distance formula.

Step-by-step solving routine

1. Start at the origin and move right for positive x or left for negative x.
2. Then move up for positive y or down for negative y.
3. For horizontal points, subtract x-values; for vertical points, subtract y-values and use a positive distance.
4. Read the plotted point back to yourself in x-then-y order.

GED® application
The points ((-3,2)) and ((5,2)) lie on the same horizontal line. Their distance is (|5-(-3)|=8) units. The equal y-values show immediately that no diagonal calculation is needed.

Coach check
Use the phrase 'across, then up or down' to prevent reversing coordinates.

Visual study gallery
Study each diagram before the worked examples. Name what is measured, identify the needed dimensions or relationships, and explain which formula or rule the picture supports.

10 worked examples and problem solving
Use these examples as guided practice before attempting the session MCQs. Each problem is self-contained, including any needed table or context.

Example 1
Problem: In the point \((4,-2)\), what is the x-coordinate?
Answer: \(4\)
Solution: The x-coordinate is the first number. Pro tip: coordinates are always written (x, y).

Example 2
Problem: In the point \((4,-2)\), what is the y-coordinate?
Answer: \(-2\)
Solution: The y-coordinate is the second number. Pro tip: coordinates are always written (x, y).

Example 3
Problem: Which point is in Quadrant I?
Answer: \((3,5)\)
Solution: Quadrant I has positive x and positive y. Pro tip: coordinates are always written (x, y).

Example 4
Problem: Which point is in Quadrant II?
Answer: \((-3,5)\)
Solution: Quadrant II has negative x and positive y. Pro tip: coordinates are always written (x, y).

Example 5
Problem: Which point is in Quadrant III?
Answer: \((-3,-5)\)
Solution: Quadrant III has negative x and negative y. Pro tip: coordinates are always written (x, y).

Example 6
Problem: Which point is in Quadrant IV?
Answer: \((3,-5)\)
Solution: Quadrant IV has positive x and negative y. Pro tip: coordinates are always written (x, y).

Example 7
Problem: What is the horizontal distance from \((2,7)\) to \((9,7)\)?
Answer: \(7\)
Solution: Only x changes, so the distance is \(9 - 2 = 7\). Pro tip: coordinates are always written (x, y).

Example 8
Problem: What is the vertical distance from \((-1,3)\) to \((-1,10)\)?
Answer: \(7\)
Solution: Only y changes, so the distance is \(10 - 3 = 7\). Pro tip: coordinates are always written (x, y).

Example 9
Problem: Which point lies on the y-axis?
Answer: \((0,6)\)
Solution: Points on the y-axis have x = \(0\). Pro tip: coordinates are always written (x, y).

Example 10
Problem: Which point lies on the x-axis?
Answer: \((6,0)\)
Solution: Points on the x-axis have y = \(0\). Pro tip: coordinates are always written (x, y).

Additional resources

• Coordinate reminder: points are written \((x,y)\); x moves left/right and y moves up/down.
• Axis check: points on the x-axis have \(y=0\); points on the y-axis have \(x=0\).