Question

Give the number of different planes that can be drawn passing through the given number of points.
1:
2:
3 COLLINEAR POINTS:

Answer 1

What do you think? Picture the number of points, and think about how many planes you can have passing through them. I think you can get these if you just think about it intuitively.

Answer 2

1 point: how many planes? what (if anything) limits the planes that can go through a single point?

Answer 3

I don't think any planes can go through just ONE point. Because a pane is a surface, and not a line?

Answer 4

Well, the question isn't whether the points given DEFINE a PARTICULAR plane. Just, how many DIFFERENT planes can be drawn that pass through the point(s).

For 1 point, picture a piece of paper balanced on the tip of a pencil. You can turn, swivel, flip the paper all around that pencil in any direction you want, right? And the paper still "passes through" the point at the tip. That paper represents all the planes that can be drawn, passing through that single point.

so how many would you say that is? (HINT: this answer isn't *really* a "number"!)

Answer 5

infinate?

Answer 6

Yes, infinitely many!

Answer 7

ok! so for 2, its the same isnt it? Because 2 pencils with paper on top is the same way!

Answer 8

Exactly... kind of! LOL! if you think about ONE plane through the 2 points, now you can just rotate that paper all the way around the line that connects those two points. You can't actually flip the paper quite as freely as with one point, but here's the thing...... that complete rotation around that line joining the points, STILL means infinitely many planes! (Kind of like how there are infinitely many points between any 2 distinct points on a number line.)

Answer 9

Now you can probably guess what happens with the 3 collinear points... if you think about what I just said about the "line segment" joining the 2 points above!

Answer 10

Thanks!!!!!

Answer 11

You're welcome. :)