3-1 (b) Distance between two points
Point 2 of 8 — The 3D Coordinate System and Vectors in SpaceQuestion bank: 0 questions (0 with pictures)
02 3-1 (b) Distance between two points
Rule
- For and :
- It comes from applying Pythagoras' theorem twice: first in the horizontal plane, then with the vertical difference.
✍️ Worked examples
Example 2: Show that the triangle , , is right-angled at .
Solution:
- .
- .
- .
- , so the angle at is .
Example 3: Show that , , form an equilateral triangle and find its area.
Solution:
- , , .
- All sides are equal, so it is equilateral.
- Area square units.
Example 4: Find if the triangle with vertices , , is equilateral.
Solution:
- Let the points be , , . .
- and , so for every (the triangle is always isosceles).
- Equilateral requires , so and .
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