A(4,7) and B (2,1), P(3,a) is the midpoint of seg AB, then the value of a is _ _ _ _ _ _

Options

A. 4
B. 8
C. 6
D. 3

Answer

To find the value of \( a \) such that point \( P(3, a) \) is the midpoint of segment \( AB \) where \( A(4, 7) \) and \( B(2, 1) \), we can use the midpoint formula. The midpoint \( M(x, y) \) of a segment with endpoints \( A(x_1, y_1) \) and \( B(x_2, y_2) \) is given by:

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

### Step 1: Identify the coordinates of points A and B
- Point \( A \) has coordinates \( (4, 7) \)
- Point \( B \) has coordinates \( (2, 1) \)

### Step 2: Apply the midpoint formula
Using the midpoint formula, we can find the coordinates of point \( P \):

\[ P = \left( \frac{4 + 2}{2}, \frac{7 + 1}{2} \right) \]

### Step 3: Calculate the x-coordinate of P
Calculating the x-coordinate:

\[ \frac{4 + 2}{2} = \frac{6}{2} = 3 \]

### Step 4: Calculate the y-coordinate of P
Calculating the y-coordinate:

\[ \frac{7 + 1}{2} = \frac{8}{2} = 4 \]

### Step 5: Set the y-coordinate equal to a
Since point \( P \) has coordinates \( (3, a) \), we can set \( a \) equal to the calculated y-coordinate:

\[ a = 4 \]

### Final Answer
Thus, the value of \( a \) is \( 4 \).

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