Distance between two points on a gridline
Sometimes you'll be given two points on a coordinate grid and asked: how far apart are they? When the two points share a coordinate — they sit on the same horizontal line or the same vertical line — the answer is easy. You don't need any clever formula; you just count squares (or do a quick subtraction).
When two points share a coordinate
Look at the two points. Compare their x-values and their y-values:
- If the y-values match, the points sit on the same horizontal line. The distance is the difference of the x-values.
- If the x-values match, the points sit on the same vertical line. The distance is the difference of the y-values.
That difference is always taken so that the answer is positive — bigger number minus smaller number.
A worked example
A is at (1, 2) and B is at (4, 2). How far apart are A and B?
Both points have y = 2, so they share a horizontal line. The distance is the difference of the x-values:
4 − 1 = 3 squares
You can also check by counting: from (1, 2) move right past (2, 2), (3, 2), then to (4, 2). That's three jumps — three squares.
P is at (5, 1) and Q is at (5, 7). How far apart are they?
Both points have x = 5, so they share a vertical line. The distance is the difference of the y-values:
7 − 1 = 6 squares
What if neither coordinate matches?
If the two points don't share an x-value or a y-value — like (1, 2) and (4, 6) — then they don't sit on a single gridline. The straight-line distance isn't a whole number of squares any more, and you'd need the Pythagorean theorem to work it out. That comes in a later year. For now, every question in this section will give you two points that share one coordinate.
A puzzle
Three points are given: A(2, 1), B(2, 5) and C(7, 1). What is the perimeter of the triangle ABC?
- AB shares x = 2, so AB = 5 − 1 = 4.
- AC shares y = 1, so AC = 7 − 2 = 5.
- BC doesn't share either coordinate — you can't measure it without Pythagoras yet.
The two sides you can measure with this technique are AB and AC.