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A kite flies at the point (6, -4, 10) in a coordinate system on a flat field…
Contributed by StemPy LabTry it on paper first. A hint, the key idea and the worked solution are here when you need them.
A kite flies at the point in a coordinate system on a flat field. The origin is at a pole. All distances are in metres. The -plane is the ground, and the -axis points up. The sun is straight overhead, so the shadow of the kite on the ground is the foot of the perpendicular from the kite to the ground. Find the -coordinate of the shadow. Then find the distance between the kite and its shadow.
Need a reminder? The key ideaShow
The foot of the perpendicular on a coordinate plane makes one coordinate zero. The image in a plane changes one sign, the image in an axis changes two signs, and the image in the origin changes all three. The foot is the midpoint of the point and its image.
The worked solution
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.
Given. The kite is at m.
Step 1. The shadow. The foot on the -plane is . Its -coordinate is .
Step 2. The distance. The kite and the shadow differ only in . The distance is .
Check. The distance is the same as the distance of the kite from the -plane, which is .
Answer: the shadow has , and it is from the kite.
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