Grade 10 · Free math lesson

Coordinate Geometry

After this lesson, you will be able to plot points, find distances, and locate midpoints on a coordinate grid.

Practice Coordinate Geometry free

Skills in this unit

Pick a skill to try three free questions on just that.

Standards covered:8.G.B.8G-GPE.B.7G-GPE.B.68.G.B.78.G.B.68.G.A.18.G.A.38.G.A.4G-SRT.A.2G-GPE.A.16.G.A.3G-GPE.B.4

Reading the Grid

A coordinate grid has two lines: the horizontal x-axis and the vertical y-axis. Every point has two numbers called coordinates — (x, y) — that tell you how far to go right/left and up/down.

Example: The point (3, 2) means: go 3 steps right, then 2 steps up from the center (origin).

Remember: Remember: x comes before y — think 'along the corridor, then up the stairs'.

Finding the Distance

The distance between two points is found using the Distance Formula: d = √[(x2−x1)² + (y2−y1)²]. You are basically measuring the diagonal of a right triangle.

Example: Distance between (1, 2) and (4, 6): d = √[(4−1)² + (6−2)²] = √[9 + 16] = √25 = 5 units.

Remember: Subtract x's, subtract y's, square both, add them, then square root — 'Subtract, Square, Add, Root'.

Finding the Midpoint

The midpoint is the exact middle between two points. Use the Midpoint Formula: M = ((x1+x2)/2, (y1+y2)/2). You just average the x's and average the y's.

Example: Midpoint of (2, 4) and (6, 8): M = ((2+6)/2, (4+8)/2) = (4, 6).

Remember: Think of it like splitting a pizza — add both shares and divide by 2.

Worked example

Point A is at (1, 3) and Point B is at (7, 11). Find the distance and midpoint between them.

  1. 1Distance: d = √[(7−1)² + (11−3)²] = √[36 + 64] = √100 = 10 units.
  2. 2Midpoint: M = ((1+7)/2, (3+11)/2) = (8/2, 14/2) = (4, 7).
  3. 3So the two points are 10 units apart, and their midpoint is (4, 7).

Answer: Distance = 10 units, Midpoint = (4, 7)

The #1 mistake to avoid

Mixing up x and y when plotting — always move LEFT or RIGHT first (x), THEN UP or DOWN (y). Never the other way around.

Key takeaways

  • Every point on a grid is written as (x, y) — right/left first, up/down second.
  • Use d = √[(x2−x1)² + (y2−y1)²] to find the distance between two points.
  • Use M = ((x1+x2)/2, (y1+y2)/2) to find the midpoint — just average the x's and y's.

Master Coordinate Geometry — free

Interactive practice you solve by doing, an AI tutor when you're stuck, and mastery you can't fake. No credit card.

Start practicing free