determine whether the points can form a line in the given plane. then, write yes or no.
1.
points r and s ______
2.
points m and n ______
3.
points a and b ______
draw and label each of the following.
4. three collinear points in plane a
5. three coplanar points in plane c
6. $overleftrightarrow{ln}$ exists in plane m
7. one point that is not coplanar to plane s
8. points d, e, f are collinear in plane a, but not in plane b
9. collinear points q, r, and s in plane

Question

Accepted Answer

### 1. Points R and S
# Answer:
Yes
# Explanation:
## Step1: Recall collinearity
Two points are always collinear (lie on a line) as a line is defined by two points.
## Step2: Apply to R and S
Since R and S are two points in the same plane, they can form a line.

### 2. Points M and N
# Answer:
No
# Explanation:
## Step1: Analyze positions
Point M is inside the plane's shape, and point N is outside (or at a position not aligned with M in a way that they lie on a line within the plane).
## Step2: Conclude collinearity
Visually, M and N do not appear to lie on a straight line within the given plane, so they cannot form a line.

### 3. Points A and B
# Answer:
Yes
# Explanation:
## Step1: Recall collinearity rule
Two points always determine a line.
## Step2: Check A and B
A and B are two points in the same plane, so they can form a line.

### 4. Three collinear points in plane A
# Answer:
(Example: Draw a straight line in plane A and label three points, say P, Q, R, on it.)
# Explanation:
## Step1: Define collinear
Collinear points lie on the same line.
## Step2: Draw in plane A
In plane A, draw a straight line segment. Mark three distinct points along this segment and label them (e.g., P, Q, R). These three points are collinear and lie in plane A.

### 5. Three coplanar points in plane C
# Answer:
(Example: Choose any three points within the region of plane C, say X, Y, Z, as all points in a plane are coplanar.)
# Explanation:
## Step1: Define coplanar
Coplanar points lie in the same plane.
## Step2: Select in plane C
Since plane C is a flat surface, any three points within the area of plane C (e.g., the vertices or any interior points) will be coplanar. Label three such points (e.g., X, Y, Z).

### 6. $\overleftrightarrow{LN}$ exists in plane M
# Answer:
(Example: Draw a line passing through points L and N such that the line lies within the boundaries of plane M.)
# Explanation:
## Step1: Understand line in plane
A line exists in a plane if the line (defined by two points) lies within the plane's region.
## Step2: Draw $\overleftrightarrow{LN}$ in plane M
Locate points L and N (L is inside the plane's shape, N is outside? Wait, no—wait, the plane's shape: if we adjust, draw a line through L and N such that the line is within plane M. So extend or draw the line segment LN (or the line) so that it lies in plane M.

### 7. One point that is not coplanar to plane S
# Answer:
(Example: A point, say T, outside the region of plane S.)
# Explanation:
## Step1: Define non - coplanar
A point not coplanar to a plane does not lie in that plane.
## Step2: Select the point
Choose a point that is clearly outside the area of plane S (e.g., a point in a different plane or outside the given plane's diagram). Label it (e.g., T).

### 8. Points D, E, F are collinear in plane A, but not in plane B
# Answer:
(Example: Draw a line in plane A with points D, E, F. Ensure this line does not intersect or lie in plane B.)
# Explanation:
## Step1: Collinear in plane A
Draw a straight line in plane A and place points D, E, F on it (so they are collinear in A).
## Step2: Not in plane B
Position plane B such that the line containing D, E, F does not lie within plane B (e.g., plane B is parallel or angled so the line is outside its region).

### 9. Collinear points Q, R, and S in plane [let's assume plane P]
# Answer:
(Example: Draw a straight line in plane P and label three points Q, R, S on it.)
# Explanation:
## Step1: Collinearity in plane
Collinear points lie on a line within the plane.
## Step2: Draw and label
In the given plane (e.g., plane P), draw a straight line. Mark three points Q, R, S along this line. These points are collinear and lie in the plane.

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

1. Points R and S

Step1: Recall collinearity

Step2: Apply to R and S

2. Points M and N

Step1: Analyze positions

Step2: Conclude collinearity

3. Points A and B

Step1: Recall collinearity rule

Step2: Check A and B

4. Three collinear points in plane A

Answer: