Try it on paper first. A hint, the key idea and the worked solution are here when you need them.
A small tent frame is a tetrahedron with corners , , and a fourth corner that was lost in the drawing. Distances are in metres. The drawing does record the centroid of the four corners, . Find the three coordinates of .
The centroid of a triangle is the mean of its 3 corners, and of a tetrahedron the mean of its 4. A parallelogram has . Points are collinear if or if one section ratio fits all three coordinates.
Have you tried it?
Work it out on paper first. It is fine to get stuck or make a mistake: that is how we learn. When you are ready, go through the solution one step at a time, and check each step against your own.
Step 1. The sums. The four -values add up to . The three known ones add up to . So .
Step 2. The -values. and . So .
Step 3. The -values. and . So .
Check. The mean of the four corners is , the recorded centroid.
Answer: .
Log in to join the discussion.
Loading…