Coordinate Plane

5.F.1Plot points (Q1)01/04

Plot points in the first quadrant.

Step01of 04

The coordinate plane is two perpendicular number lines: the horizontal x-axis and the vertical y-axis. They cross at the origin (0, 0). The first quadrant is the upper-right region where both x and y are positive.

5.F.1 — Plot points in the first quadrant.

Step 01 of 04

Step 02 of 04

A point is named by an ordered pair $(x, y)$ . The first number is the horizontal position, the second is the vertical.

(0, 0)	→origin (where axes meet)
(3, 0)	→3 right, 0 up — on the x-axis
(0, 4)	→0 right, 4 up — on the y-axis
(2, 5)	→2 right, 5 up — somewhere in Quadrant 1

Step 03 of 04

Recipe to plot. Start at the origin. Move x units RIGHT (first coordinate). Move y units UP (second coordinate). Mark the point.

Step 04 of 04

Order matters! (3, 5) and (5, 3) are DIFFERENT points. Always read the first coordinate as horizontal, second as vertical.

Key insight

Ordered pair (x, y): first is horizontal, second is vertical. Start at origin, count right then up. Order matters — switching gives a different point.

5.F.2 — Read coordinates from a graph.

Step 01 of 04

Reverse of plotting. From a marked point, count how many units RIGHT of the y-axis (= x-coordinate) and how many UP from the x-axis (= y-coordinate).

Step 02 of 04

Worked examples. Read these points off a Q1 grid.

Point 4 right, 2 up	→(4, 2)
Point on y-axis at 5	→(0, 5)
Point on x-axis at 3	→(3, 0)

Step 03 of 04

Common error: swapping x and y. Always read horizontal first.

Step 04 of 04

If a point has fractional coordinates, count using the gridlines as references. (1.5, 2) is halfway between x = 1 and x = 2, vertically aligned with y = 2.

Key insight

Read horizontal-then-vertical. If a point isn't on a gridline, use halves or quarters of grid spacing. Always (x, y), never (y, x).

5.F.3 — Coordinate-plane word problems.

Step 01 of 04

Real-world contexts often map to the coordinate plane: time vs. distance, temperature vs. day, grids on maps. The x-axis usually represents the INDEPENDENT variable (time, day) and y-axis the DEPENDENT one.

Step 02 of 04

Worked example. A car's distance from home (in miles) over time (in hours): (0, 0), (1, 30), (2, 65), (3, 90).

Plot these and read the trip story: starts at home, drives 30 mi the first hour, 35 mi the second hour, 25 mi the third.

Step 03 of 04

Distance between two points on the SAME ROW or COLUMN is just the difference in the other coordinate.

(2, 5) to (7, 5)	→same y — distance = 7 − 2 = 5
(3, 1) to (3, 8)	→same x — distance = 8 − 1 = 7

Step 04 of 04

Word problem. A school is at (4, 2). The library is at (4, 9). How far apart (in grid units)?

9 - 2 = 7 units

Key insight

Coordinate planes model real situations. x-axis is usually time / independent. Same row or column → distance is just the coordinate difference. Always include units in your answer.

Free diagnostic

Test your understanding: 10 questions, ~10 min.

Pulled live from our bank for 5.F · scored instantly with worked solutions · free, no sign-up.

Start diagnostic →Print worksheets

5.F.1 – 5.F.3 · CCSS 5.G.A · Full curriculum →