Use the diagram to the right to answer 1-4. 1. Name two points collinear to point D. 2. Give another name for line p. 3. Name the intersection of line r and plane K. 4. Name a point non-coplanar to plane K 4 5′
The Correct Answer and Explanation is:
1. Name two points collinear to point D.
Answer: Points E and Q are collinear with point D.
Explanation:
Points are collinear if they lie on the same straight line. In the diagram, points D, E, and Q lie along the same line (line q). Since these three points form a straight line segment in the plane, they are collinear. Point E is between D and Q, showing linear alignment.
2. Give another name for line p.
Answer: Line AB is another name for line p.
Explanation:
Line p passes through points A and B, as seen in the diagram. Lines can be named using any two distinct points that lie on them. Therefore, line AB is a valid alternate name for line p. This follows the naming convention in geometry where lines are denoted either by lowercase letters or two points lying on the line.
3. Name the intersection of line r and plane K.
Answer: Point X is the intersection of line r and plane K.
Explanation:
In the diagram, line r is a vertical line that intersects the parallelogram-shaped plane K. The point at which line r crosses the plane is marked as point X. This is the definition of the intersection between a line and a plane — the point where they meet.
4. Name a point non-coplanar to plane K.
Answer: Point W is non-coplanar to plane K.
Explanation:
A point is non-coplanar if it does not lie on the same plane. Plane K includes all the points forming the parallelogram (like A, B, D, E, F, etc.). Point W, however, lies above the plane (as line r is perpendicular or slanted relative to the plane), making it non-coplanar. Points on a line intersecting a plane but not lying in it (like W) are outside that plane.
Summary:
- 1. D, E, Q are collinear.
- 2. Line AB = line p.
- 3. Line r intersects plane K at point X.
- 4. Point W is not on plane K, hence non-coplanar.
These answers show understanding of geometric concepts like collinearity, line naming, line-plane intersections, and coplanarity.
