Question

a point that is not coplanar with plane a.
in exercises 9–11, sketch the figure described.

1. plane a and line $overline{bc}$ intersecting at point c
2. plane m and plane n not intersecting
3. lines a, b, and c intersecting at three points
4. a tripod can be used to level a camera. what geometric figure is modeled by the intersection of a tripod to the ground? explain.

in exercises 13 and 14, graph the inequality on a number line. tell whether the graph is a segment, a ray or rays, a point, or a line.

1. $x \geq 2$
2. $-4 < x < 4$

Explanation:

Question 13: \( x \geq 2 \)

Step 1: Identify the inequality type

The inequality is \( x \geq 2 \), which means all real numbers greater than or equal to 2.

Step 2: Graph on number line

• Draw a number line.
• Locate the point 2. Since \( x \) can be equal to 2, we use a closed circle (or a filled dot) at 2.
• Then, draw an arrow starting from the closed circle at 2 and pointing to the right (towards positive infinity) to represent all numbers greater than 2.

Step 3: Determine the graph type

A ray starts at a point and extends infinitely in one direction. Here, the graph starts at 2 (inclusive) and goes infinitely to the right, so it is a ray.

Step 1: Identify the inequality type

The inequality is \( -4 < x < 4 \), which means all real numbers greater than -4 and less than 4.

Step 2: Graph on number line

• Draw a number line.
• Locate the points -4 and 4. Since \( x \) is not equal to -4 or 4, we use open circles (or unfilled dots) at -4 and 4.
• Then, draw a line segment connecting the open circles at -4 and 4 to represent all numbers between -4 and 4.

Step 3: Determine the graph type

A segment is a part of a line between two endpoints. Here, the graph is between -4 (exclusive) and 4 (exclusive), so it is a segment.

Answer:

The graph of \( x \geq 2 \) on a number line has a closed circle at 2 and an arrow to the right. The graph is a ray.

Question 14: \( -4 < x < 4 \)