Question

1. choose the best answer.

calculate the length of segment \\( \overline{ad} \\) with midpoint \\( m \\) when \\( am = 8 \\).
\\( \bigcirc \\) 64
\\( \bigcirc \\) 4
\\( \bigcirc \\) 16
\\( \bigcirc \\) 8

1. choose the best answer.

calculate the length of segment \\( \overline{rs} \\) with midpoint \\( m \\) when \\( rm = 2x \\) and \\( ms = x + 5 \\).
\\( \bigcirc \\) 4
\\( \bigcirc \\) 5
\\( \bigcirc \\) 10
\\( \bigcirc \\) 20

Explanation:

Question 9

Step1: Recall midpoint definition

A midpoint divides a segment into two equal parts, so \( AM = MB \) and \( AB = AM + MB \).

Step2: Calculate \( AB \)

Given \( AM = 8 \), then \( MB = 8 \) (since \( M \) is midpoint). So \( AB = AM + MB = 8 + 8 = 16 \).

Step1: Use midpoint property

Since \( M \) is midpoint of \( RS \), \( RM = MS \).

Step2: Solve for \( x \)

Given \( RM = 2x \) and \( MS = x + 5 \), set \( 2x = x + 5 \). Subtract \( x \) from both sides: \( 2x - x = x + 5 - x \) → \( x = 5 \).

Step3: Find \( RM \) and \( RS \)

\( RM = 2x = 2(5) = 10 \). Then \( RS = RM + MS = 10 + 10 = 20 \) (since \( RM = MS \)).

Answer:

16

Question 10