Coordinate Geometry: Find the Hidden Point
Understand that a point is located by an ordered pair, x across first and y up or down second, and that the signs of the two coordinates decide which quadrant the point lies in.
Before you try
What if you swapped the two numbers in a pair? Would you land in the same place?
Try it out
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What happened?
Move a control to see what changes and why.
Points land exactly on grid lines. Real measurements rarely fall on whole numbers.
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Try these ideas
- Plot (3, 4), then (−3, 4) and compare their quadrants.
- Turn on the path from the origin and follow the across-then-up route.
- Press New hidden point and find it in as few moves as you can.
Why it works
Two number lines crossing at right angles turn a flat page into a map. The horizontal line is the x axis, the vertical one is the y axis, and where they cross is the origin, written (0, 0). To find a point you always go across first and then up or down, which is why order matters: (3, 5) and (5, 3) are two different places.
The axes cut the plane into four quadrants, numbered anticlockwise from the top right. Their signs are (+, +), (−, +), (−, −) and (+, −), so the signs alone tell you where a point sits. A point with a zero coordinate lies on an axis and belongs to no quadrant. In this simulator you move a point with sliders or by clicking, and a hidden-point game gives you a step count and a direction hint after each move.
Check your understanding
Question 1 of 4
Which point is in quadrant II?
In the pair (7, 2), what does the 7 tell you?
Where does the point (0, 5) lie?
Are (2, 6) and (6, 2) the same point?
Explain it in your own words
What changed? Why did it happen? Where might you notice this in everyday life?
What will you discover next?
Try Geometric Transformations: Move, Flip and Turn next.
For parents & teachers
- Play battleships on squared paper and call out coordinates.
- Find a place on a map using its grid reference.
- Ask where quadrant III would be on a graph of temperature against time.