To find the distance from the midpoint of PR to point Q, we will follow these steps:
1. Find the midpoint, M, of the line segment PR.
2. Calculate the distance between the midpoint, M, and point Q.
3. Round the result to the nearest hundredth.
First, let's find the midpoint of PR:
The coordinates of point P (3, -8) and the coordinates of point R (-1, 4) are given. The midpoint M of PR has coordinates \((M_x, M_y)\) that can be found using the midpoint formula:
\[ M_x = \frac{P_x + R_x}{2}, \quad M_y = \frac{P_y + R_y}{2} \]
where \( (P_x, P_y) \) are the coordinates of point P and \( (R_x, R_y) \) are the coordinates of point R.
Plugging in the values:
\[ M_x = \frac{3 + (-1)}{2} = \frac{2}{2} = 1 \]
\[ M_y = \frac{-8 + 4}{2} = \frac{-4}{2} = -2 \]
So the coordinates of the midpoint M of line segment PR are (1, -2).
Next, let's calculate the distance from M to Q using the distance formula:
\[ \text{Distance} = \sqrt{(Q_x - M_x)^2 + (Q_y - M_y)^2} \]
where \( (M_x, M_y) \) are the coordinates of the midpoint M, and \( (Q_x, Q_y) \) are the coordinates of point Q.
The coordinates of point Q are (-3, 1), so plugging in the values:
\[ \text{Distance} = \sqrt{(-3 - 1)^2 + (1 - (-2))^2} \]
\[ \text{Distance} = \sqrt{(-4)^2 + (3)^2} \]
\[ \text{Distance} = \sqrt{16 + 9} \]
\[ \text{Distance} = \sqrt{25} \]
\[ \text{Distance} = 5 \]
Therefore, the distance from the midpoint of PR to point Q is 5 units. Since the distance is already a whole number, there is no need to round to the nearest hundredth in this case; it remains 5.00 when expressed to the nearest hundredth.
