The mid-point of the line segment joining the points (- 2, 4) and (6, 10) is

Options

A. (2, 5)
B. (2, 7)
C. (3, 7)
D. (3, 8)

Answer

To find the midpoint of the line segment joining the points (-2, 4) and (6, 10), we can use the midpoint formula. The midpoint \( M \) of a line segment joining two points \( (x_1, y_1) \) and \( (x_2, y_2) \) is given by:

\[ M = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right) \]

### Step 1: Identify the coordinates
We have two points:
- Point 1: \( (x_1, y_1) = (-2, 4) \)
- Point 2: \( (x_2, y_2) = (6, 10) \)

### Step 2: Substitute the coordinates into the midpoint formula
Now, we will substitute the values of \( x_1, y_1, x_2, \) and \( y_2 \) into the midpoint formula.

\[ M = \left( \frac{-2 + 6}{2}, \frac{4 + 10}{2} \right) \]

### Step 3: Calculate the x-coordinate of the midpoint
Calculate the x-coordinate:

\[ \frac{-2 + 6}{2} = \frac{4}{2} = 2 \]

### Step 4: Calculate the y-coordinate of the midpoint
Now calculate the y-coordinate:

\[ \frac{4 + 10}{2} = \frac{14}{2} = 7 \]

### Step 5: Combine the results to find the midpoint
Now we can combine the x and y coordinates to find the midpoint:

\[ M = (2, 7) \]

Thus, the midpoint of the line segment joining the points (-2, 4) and (6, 10) is \( (2, 7) \).

### Final Answer
The midpoint is \( (2, 7) \).

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