Question

1. choose the best answer.

calculate the length of segment \\( \overline { a b } \\) with midpoint, \\( m \\), if \\( \overline { a m } = 5 \\).
1
10
20
25

1. choose the best answer.

calculate the length of segment \\( \overline { r s } \\) with midpoint, \\( m \\), if \\( \overline { r m } = 5 x \\) and \\( \overline { m s } = x + 12 \\)
30
36
15
25

Explanation:

Step1: Use the mid - point property

Since \(M\) is the mid - point of \(\overline{AB}\), we know that \(AB = 2AM\).

Step2: Substitute the value of \(AM\)

Given \(AM = 5\), then \(AB=2\times5\).

for the second problem:

Step1: Use the mid - point property

Since \(M\) is the mid - point of \(\overline{RS}\), we have \(RM = MS\). So, \(5x=x + 12\).

Step2: Solve the equation for \(x\)

Subtract \(x\) from both sides: \(5x-x=x + 12-x\), which gives \(4x=12\). Then divide both sides by \(4\): \(x=\frac{12}{4}=3\).

Step3: Find the length of \(RM\) and \(MS\)

Substitute \(x = 3\) into \(RM = 5x\), we get \(RM=5\times3 = 15\). Substitute \(x = 3\) into \(MS=x + 12\), we get \(MS=3 + 12=15\).

Step4: Calculate the length of \(RS\)

Since \(RS=RM + MS\), then \(RS=15+15\).

Answer:

\(10\)