The coordinate of the middle point of the line joining the points `(-1,-1,1)and(-1,1,-1)` are

Options

A. `(0,0,0)`
B. `(-1,0,0)`
C. `(0,-1,1)`
D. `(0,1,-1)`

Answer

To find the coordinates of the midpoint of the line segment joining the points \((-1, -1, 1)\) and \((-1, 1, -1)\), we can follow these steps:

### Step 1: Identify the coordinates of the endpoints
The coordinates of the endpoints are:
- Point 1: \((x_1, y_1, z_1) = (-1, -1, 1)\)
- Point 2: \((x_2, y_2, z_2) = (-1, 1, -1)\)

### Step 2: Use the midpoint formula
The formula for the midpoint \(M(x, y, z)\) of a line segment joining two points \((x_1, y_1, z_1)\) and \((x_2, y_2, z_2)\) is given by:
\[ M = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2}, \frac{z_1 + z_2}{2} \right) \]

### Step 3: Calculate the x-coordinate of the midpoint
Using the x-coordinates:
\[ x = \frac{x_1 + x_2}{2} = \frac{-1 + (-1)}{2} = \frac{-2}{2} = -1 \]

### Step 4: Calculate the y-coordinate of the midpoint
Using the y-coordinates:
\[ y = \frac{y_1 + y_2}{2} = \frac{-1 + 1}{2} = \frac{0}{2} = 0 \]

### Step 5: Calculate the z-coordinate of the midpoint
Using the z-coordinates:
\[ z = \frac{z_1 + z_2}{2} = \frac{1 + (-1)}{2} = \frac{0}{2} = 0 \]

### Step 6: Combine the coordinates to get the midpoint
Thus, the coordinates of the midpoint \(M\) are:
\[ M = (-1, 0, 0) \]

### Final Answer
The coordinates of the midpoint of the line joining the points \((-1, -1, 1)\) and \((-1, 1, -1)\) are \((-1, 0, 0)\).

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