An easy question on counting shapes for P2–P3, with a step-by-step solution, diagrams and the answer. Every year of the Hua Xia Cup, P1 to P6, has shape-counting questions. The hard part is counting each shape once and missing none.
The question
Two lines start from point O.
Apart from O, the across line has 2 points on it and the slanting line has 2, as shown.
A segment must lie along a drawn line, and both its ends must be points in the picture.
How many segments are there in the picture?
Show the hints (2)
💡Hint 1: Count each line on its own and add at the end. How many points does each line have, O included?
💡Hint 2: With 3 points on a line, 2 segments start at the leftmost point, 1 at the next… one fewer each time.
Worked solution
Have a go first, then read the solution step by step.
1.The across line has 3 points (O included). From one end, each point makes a segment with every point after it (the numbers in the picture): 2 + 1 = 3 segments.
2.The slanting line has 3 points (O included). From one end, each point makes a segment with every point after it (the numbers in the picture): 2 + 1 = 3 segments.
3.3 + 3 = 6 segments in all.
⚠️Common mistake: leaving out O, or joining a point on one line to a point on the other. Those segments aren't drawn, so they don't count.
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