Questions: P=(9,1,7) Q=(10,6,9) Find M, the midpoint of PQ. M=

Transcript text: P=(9,1,7) Q=(10,6,9) Find $M$, the midpoint of $\overline{P Q}$. \[ M= \]

Solution

Solution Steps

Step 1: Identify the Coordinates of Points $P$ and $Q$

The coordinates of point $P$ are given as $P = (9, 1, 7)$ and the coordinates of point $Q$ are given as $Q = (10, 6, 9)$.

Step 2: Apply the Midpoint Formula

To find the midpoint $M$ of the line segment $\overline{PQ}$ in three-dimensional space, we use the midpoint formula: \[ M = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2}, \frac{z_1 + z_2}{2} \right) \] Substituting the coordinates of $P$ and $Q$ into the formula, we have: \[ M = \left( \frac{9 + 10}{2}, \frac{1 + 6}{2}, \frac{7 + 9}{2} \right) \]

Step 3: Calculate the Midpoint Coordinates

Perform the calculations for each coordinate: \[ M_x = \frac{9 + 10}{2} = \frac{19}{2} = 9.5 \] \[ M_y = \frac{1 + 6}{2} = \frac{7}{2} = 3.5 \] \[ M_z = \frac{7 + 9}{2} = \frac{16}{2} = 8.0 \]

Final Answer

The midpoint $M$ of the line segment $\overline{PQ}$ is: \[ \boxed{(9.5, 3.5, 8.0)} \]

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