Question

a) midpoint of \\(\overline{pq}\\) : \\(-5\\) d) midpoint of \\(\overline{ru}\\) : \\(\\______\\)\
b) midpoint of \\(\overline{qt}\\) : \\(\\______\\) e) midpoint of \\(\overline{vr}\\) : \\(\\______\\)\
c) midpoint of \\(\overline{rs}\\) : \\(\\______\\) f) midpoint of \\(\overline{vq}\\) : \\(\\______\\)

Explanation:

for the midpoints, we first identify the coordinates of each point from the number line:

• \( P = -16 \)
• \( V = -10 \) (since it's 2 units right of -12)
• \( R = -4 \)
• \( Q = 6 \) (since it's 1 unit right of 4)
• \( S = 12 \)
• \( U = 20 \)
• \( T = 26 \) (since it's 3 units right of 24)

Part (b): Midpoint of \( \overline{QT} \)

The midpoint formula is \( \text{Midpoint} = \frac{x_1 + x_2}{2} \).
For \( Q = 6 \) and \( T = 26 \):

Step 1: Apply the midpoint formula

\( \text{Midpoint} = \frac{6 + 26}{2} \)

Step 2: Simplify

\( \frac{32}{2} = 16 \)

Part (c): Midpoint of \( \overline{RS} \)

For \( R = -4 \) and \( S = 12 \):

Step 1: Apply the midpoint formula

\( \text{Midpoint} = \frac{-4 + 12}{2} \)

Step 2: Simplify

\( \frac{8}{2} = 4 \)

Part (d): Midpoint of \( \overline{RU} \)

For \( R = -4 \) and \( U = 20 \):

Step 1: Apply the midpoint formula

\( \text{Midpoint} = \frac{-4 + 20}{2} \)

Step 2: Simplify

\( \frac{16}{2} = 8 \)

Part (e): Midpoint of \( \overline{VR} \)

For \( V = -10 \) and \( R = -4 \):

Step 1: Apply the midpoint formula

\( \text{Midpoint} = \frac{-10 + (-4)}{2} \)

Step 2: Simplify

\( \frac{-14}{2} = -7 \)

Part (f): Midpoint of \( \overline{VQ} \)

For \( V = -10 \) and \( Q = 6 \):

Step 1: Apply the midpoint formula

\( \text{Midpoint} = \frac{-10 + 6}{2} \)

Step 2: Simplify

\( \frac{-4}{2} = -2 \)

Final Answers:

b) \( \boldsymbol{16} \)
c) \( \boldsymbol{4} \)
d) \( \boldsymbol{8} \)
e) \( \boldsymbol{-7} \)
f) \( \boldsymbol{-2} \)

Answer:

for the midpoints, we first identify the coordinates of each point from the number line:

• \( P = -16 \)
• \( V = -10 \) (since it's 2 units right of -12)
• \( R = -4 \)
• \( Q = 6 \) (since it's 1 unit right of 4)
• \( S = 12 \)
• \( U = 20 \)
• \( T = 26 \) (since it's 3 units right of 24)

Part (b): Midpoint of \( \overline{QT} \)

The midpoint formula is \( \text{Midpoint} = \frac{x_1 + x_2}{2} \).
For \( Q = 6 \) and \( T = 26 \):

Step 1: Apply the midpoint formula

\( \text{Midpoint} = \frac{6 + 26}{2} \)

Step 2: Simplify

\( \frac{32}{2} = 16 \)

Part (c): Midpoint of \( \overline{RS} \)

For \( R = -4 \) and \( S = 12 \):

Step 1: Apply the midpoint formula

\( \text{Midpoint} = \frac{-4 + 12}{2} \)

Step 2: Simplify

\( \frac{8}{2} = 4 \)

Part (d): Midpoint of \( \overline{RU} \)

For \( R = -4 \) and \( U = 20 \):

Step 1: Apply the midpoint formula

\( \text{Midpoint} = \frac{-4 + 20}{2} \)

Step 2: Simplify

\( \frac{16}{2} = 8 \)

Part (e): Midpoint of \( \overline{VR} \)

For \( V = -10 \) and \( R = -4 \):

Step 1: Apply the midpoint formula

\( \text{Midpoint} = \frac{-10 + (-4)}{2} \)

Step 2: Simplify

\( \frac{-14}{2} = -7 \)

Part (f): Midpoint of \( \overline{VQ} \)

For \( V = -10 \) and \( Q = 6 \):

Step 1: Apply the midpoint formula

\( \text{Midpoint} = \frac{-10 + 6}{2} \)

Step 2: Simplify

\( \frac{-4}{2} = -2 \)

Final Answers:

b) \( \boldsymbol{16} \)
c) \( \boldsymbol{4} \)
d) \( \boldsymbol{8} \)
e) \( \boldsymbol{-7} \)
f) \( \boldsymbol{-2} \)