Question

decide whether each set of points determines a plane. circle yes or no.
1.

• a • b

yes no
2.

• c • e
• d

yes no
3.

• f • g • h

yes no
4.

• i

yes no
identify the points in each figure as coplanar or not coplanar.
5.

• parallelogram with two interior points, one exterior point

____________
6.
rectangle with three interior points
____________
7.
parallelogram with two interior points, one exterior point •
____________
8.
rectangle with three interior points
____________

Explanation:

Question 1:

Step1: Recall the plane - determining postulate

A plane is determined by three non - collinear points. For two points (A and B), there are infinitely many planes that can contain these two points. So two points do not determine a unique plane.

Question 2:

Step1: Recall the plane - determining postulate

A plane is determined by three non - collinear points. Here we have three points (C, D, E). But we need to check if they are non - collinear? Wait, no, actually, three non - collinear points determine a plane. But first, let's think about the number of points. Wait, three points: if they are collinear, there are infinitely many planes containing them. But in general, for three points, if we assume they are non - collinear, they determine a plane. Wait, maybe I made a mistake. Wait, the problem is "Decide whether each set of points determines a plane". For three points: if they are non - collinear, they determine a unique plane. But in question 2, we have three points C, D, E? Wait, no, looking at the diagram, maybe it's three points? Wait, no, the first question has two points (A and B), the second has three points (C, D, E)? Wait, no, the original problem:

1. Two points (A, B): Two points do not determine a unique plane (infinitely many planes can contain two points). So answer is No.

1. Three points (C, D, E): Wait, no, maybe the second set has three points? Wait, the user's diagram: for question 2, there are three points? Wait, no, the first question: A and B (two points), second: C, D, E (three points)? Wait, no, maybe I misread. Wait, the problem says "Decide whether each set of points determines a plane. Circle Yes or No."

For a set of points to determine a plane:

• A single point: infinitely many planes, so no.

• Two points: infinitely many planes, so no.

• Three non - collinear points: determine a unique plane.

• Three collinear points: infinitely many planes, so no.

• Four or more points: may or may not be coplanar, but to determine a plane, we need three non - collinear points.

So let's re - analyze:

1. Points A and B (two points): Two points do not determine a unique plane. So answer: No.

1. Points C, D, E (three points): If they are collinear, no; if non - collinear, yes. But from the diagram (assuming it's three points, maybe collinear? Wait, the original problem's diagram: for question 2, maybe three points? Wait, maybe the second set has three points, but if they are collinear, they don't determine a plane. But maybe the problem is:

Wait, the first question: two points (A, B) → No.

Second question: three points (C, D, E) → If they are non - collinear, yes; but maybe in the diagram, they are collinear? Wait, maybe I made a mistake. Wait, the standard rule: Three non - collinear points determine a plane. Two points: no. One point: no.

So:

1. Two points (A, B): No.

1. Three points (C, D, E): Wait, maybe the second set has three points, but if they are collinear, no. But maybe the problem is that for three points, if we don't know if they are collinear, but the general rule is that three non - collinear points determine a plane. But maybe in the problem, the second set is three points, but the answer is No? Wait, maybe I misread the number of points. Let's check the original problem again:

"1. A B Yes No

1. C E D Yes No

1. F G H Yes No

1. I Yes No"

Ah! So:

1. Two points (A, B): No (two points don't determine a plane).

1. Three points (C, D, E): If they are non - collinear, they determine a plane. But maybe in the diagram, they are collinear? Wait, no, three non - collinear points determine a plane. But maybe the problem is that for three points, the answer is Yes? Wait, no, let's recall the postulate: Through any three non - collinear points, there is exactly one plane. So if the three points are non - collinear, they determine a plane. But if they a…

Step1: Recall the definition of coplanar

Coplanar points are points that lie on the same plane. In the figure, one point is outside the parallelogram (the plane of the parallelogram) and two points are inside the parallelogram. So the three points do not all lie on the same plane.

Question 6:

Answer:

No