Class 8 to 11 · 28 games
Doing geometry with numbers, by giving every point an address.
In everyday life: A seat number in a cinema: row 7, seat 12. Two numbers pin down exactly one place, and you can work out how far apart two seats are without walking it.
Every point on a straight-line graph is a pair of numbers that fit the same rule. Pick a value along the bottom, go up to the line, and read across: that is the value that goes with it. Two numbers you can see at once, instead of a calculation you have to do.
Go across, then up. Those two steps and the straight line between the points make a right-angled triangle, so the distance squared is (change in x)² + (change in y)².
The slope is how far the line rises for each step across — rise over run. The intercept is where it cuts the y-axis. Those two numbers are the whole line: y = mx + c.
A circle is every point the same distance from the centre, which makes its equation x² + y² = r². Stretch it and you get an ellipse. These are the conic sections, and each one is a rule about distance written as an equation.
A is (1, 1) and B is (4, 5). How long is AB, and where is its midpoint?
AB = 5, midpoint (2.5, 3)
From A to B is 3 across and 4 up, so AB² = 9 + 16 = 25 and AB = 5. The midpoint is the average of each coordinate: x is (1 + 4) ÷ 2 = 2.5, and y is (1 + 5) ÷ 2 = 3.
You will plot points, find where lines cross, and work out distances, slopes and the shapes of curves.
Class 8 coordinate geometry (6) · Class 10 coordinate geometry (4) · Class 11 coordinate geometry (18)
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