Lesson Guide
Explanation
A point on the plane is written as two numbers in brackets, and the order matters: across first, then up. The point three comma two means go three along the bottom and then two up. Two comma three is a different place altogether. Along the corridor, then up the stairs is the phrase to keep in mind, and nought comma nought is the origin, the corner where the two axes meet.
Your Turn
Where is the point (4, 1)? Check: 4 along the bottom, then 1 up.
Watch Out
(2, 3) and (3, 2) are different points. The order is never optional.
Explanation
To read a point off the grid, drop straight down from it to the bottom axis for the first number, then go straight across to the side axis for the second. A point that sits high up near the left has a small first number and a large second one, which is exactly the pair people swap. Say it aloud — two across, five up — and then write it down.
Your Turn
A point is 5 along and 1 up. Write its coordinates. Check: (5, 1).
Watch Out
A point high on the grid has a big SECOND number, not a big first one.
Explanation
Points that share their first number stand one above another in a column; points that share their second number stand side by side in a row. That is the quickest way to find a missing corner, because the fourth corner of a rectangle shares its first number with one neighbour and its second with the other. And the distance along a row is just the difference of the first numbers: from two comma three to six comma three is four units.
Your Turn
How far apart are (2, 3) and (6, 3)? Check: 6 − 2 = 4 units.
Watch Out
Subtract the numbers that DIFFER. Along a row the second numbers match, so the gap comes from the first ones.
Explanation
When a question gives a set of points and asks what shape they make, plot them first — the picture answers it immediately. One comma one, five comma one, five comma four and one comma four make a shape four units across and three units up, which is a rectangle but not a square. And once it is plotted you can read off the perimeter and the area as well: fourteen units round, twelve square units inside.
Your Turn
What is the area of that rectangle? Check: 4 × 3 = 12 square units.
Watch Out
Count units between the points, not the points themselves. From x = 1 to x = 5 is 4 units, not 5.
Explanation
The missing-corner question is the one worth practising. Three corners of a rectangle are given, and the fourth shares its first number with one of them and its second with another. With one comma one, five comma one and five comma four, the fourth corner takes the one from the first point and the four from the third: one comma four. Then the area follows from the two side lengths. Quiz and exercises now.
Your Turn
Three corners are (2, 1), (6, 1) and (6, 5). What is the fourth? Check: (2, 5).
Watch Out
Check your fourth corner makes a rectangle, not a zigzag. Two of its neighbours must line up with it.
📌 Key Points — this lesson in a nutshell
- A point is written (across, up) — the x value first, then the y value.
- (0, 0) is the origin, where the two axes cross.
- Points with the same x sit one above the other; points with the same y sit in a row.
- To name a shape from its corners, plot them first — the picture answers the question.
Step 1: Introduction
Step 1 of 5
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