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 +