Foundation and Higher · coordinates

Two points.
Can you find the
middle and the
distance?

no formula
to memorise

one pair of points, two questions —

A to B

where is the middle?

how long is the line?

question 1 of 2

Midpoint

1. x: halfway from −3 to 5. (−3 + 5) ÷ 2 = 1

2. y: halfway from −1 to 5. (−1 + 5) ÷ 2 = 2

✓ Midpoint (1, 2): the mean of the x’s,
the mean of the y’s

question 2 of 2

1. Make a right-angled triangle.

2. Count the sides: 8 across, 6 up.

3. Pythagoras: 8² + 6² = 64 + 36 = 100.

✓ AB = √100 = 10

two points, two tools —

Midpoint

the mean of each coordinate

Length

Pythagoras on the two gaps

The gap from −3 to 5 is 8, not 2 —
count it on the grid.

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