https://file.aiquickdraw.com/mathbot/file/17280491772715kbx3aax.jpg

Let's go through the questions in the image you uploaded. Here's how we can solve them step-by-step:

### 1. **Find \( QS \) and explain how you found the answer.**

In the image, we have points \( Q \), \( R \), and \( S \) on a line:
- \( Q = 12 \)
- \( R = 19 \)

So the length \( QR = 19 - 12 = 7 \).

We are looking for \( QS \). Since \( S \) is farther than \( R \) from \( Q \), it would follow the same process:
- \( S = 47 \)
Thus, \( QS = 47 - 12 = 35 \).

### 2. **Find \( QS \) when given segment lengths.**

We are given the total segment \( QR = 59 \) and part of the segment \( RS = 47 \). To find \( QS \), we add these two lengths:
\[ QS = QR + RS = 59 + 47 = 106. \]

### 3. **Find the midpoint of \( AB \) and the length of \( AB \).**

We are given:
- \( A(-4, -8) \)
- \( B(-1, 4) \)

#### To find the midpoint \( M \):
The midpoint formula is:
\[
M = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right)
\]
Substitute the values:
\[
M = \left( \frac{-4 + (-1)}{2}, \frac{-8 + 4}{2} \right) = \left( \frac{-5}{2}, \frac{-4}{2} \right) = \left( -2.5, -2 \right)
\]

#### To find the length of \( AB \):
The distance formula is:
\[
d = \sqrt{(x_2 - x_1)^2 +

Solve problems related to finding distances on number lines, midpoint of a line segment, and checking collinearity and other geometric properties.

This problem focuses on finding distances on a number line, calculating the midpoint of a line segment using the midpoint formula, and determining the collinearity of points. Suitable for students in Grades 9-10.

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