Question

explain each of the following. draw if possible:

1. $overline{pq}$
2. $overleftrightarrow{pq}$
3. plane pqr
4. pq
5. what are the two ways to name a line?
6. what are the two ways to name a plane?
7. how do you name a segment?

use the diagram on the right for the questions 8 – 12 below.

1. name $overleftrightarrow{ac}$ two more ways.
2. what is coplanar? name four coplanar points.
3. what is collinear? name three collinear points.
4. name the intersection of plane n and plane f.
5. what is another name for plane n.
6. describe the process used to find the distance between two points, then find the distance.

diagram for 13: coordinate grid with p(-2,2) and q(5,8)

Explanation:

Question 13 Solution:

Step1: Recall Distance Formula

The distance \( d \) between two points \( (x_1, y_1) \) and \( (x_2, y_2) \) is given by the formula:
\( d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \)

Step2: Identify Coordinates

For points \( P(-2, 2) \) and \( Q(5, 8) \), we have:
\( x_1 = -2, \, y_1 = 2 \)
\( x_2 = 5, \, y_2 = 8 \)

Step3: Substitute into Formula

Calculate \( x_2 - x_1 \) and \( y_2 - y_1 \):
\( x_2 - x_1 = 5 - (-2) = 7 \)
\( y_2 - y_1 = 8 - 2 = 6 \)

Then, substitute into the distance formula:
\( d = \sqrt{(7)^2 + (6)^2} = \sqrt{49 + 36} = \sqrt{85} \)

Answer:

To find the distance between two points \( (x_1, y_1) \) and \( (x_2, y_2) \), use the distance formula \( d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \). For \( P(-2, 2) \) and \( Q(5, 8) \), the distance is \( \sqrt{85} \) (or approximately \( 9.22 \)).