Question

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

Explanation:

To solve for the midpoints, we use the midpoint formula for two points \( x_1 \) and \( x_2 \) on a number line: \( \text{Midpoint} = \frac{x_1 + x_2}{2} \). First, we identify the coordinates of each point from the number line:

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

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

• \( Q = 6 \), \( T = 26 \)

Step1: Apply midpoint formula

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

Step2: Calculate the sum and divide by 2

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

Answer:

(b): \( 16 \)

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

• \( R = -4 \), \( S = 12 \)

Step1: Apply midpoint formula

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

Step2: Calculate the sum and divide by 2

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