Find the coordinates of S, if S is the midpoint of line joining `A(-3,7)` and `D(9,1)`.

Options

A. `(-1,1)`
B. `(1,-1)`
C. `(-2,2)`
D. `(3,4)`

Answer

To find the coordinates of point S, which is the midpoint of the line segment joining points A(-3, 7) and D(9, 1), we can use the midpoint formula. The midpoint \( S(x, y) \) of a line segment joining two points \( A(x_1, y_1) \) and \( D(x_2, y_2) \) is given by:

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

### Step 1: Identify the coordinates of points A and D
Here, the coordinates of point A are \( (-3, 7) \) and the coordinates of point D are \( (9, 1) \).

### Step 2: Apply the midpoint formula
Using the midpoint formula, we can find the x-coordinate and y-coordinate of point S.

1. **Calculate the x-coordinate of S:**
\[ x = \frac{x_1 + x_2}{2} = \frac{-3 + 9}{2} \]
\[ x = \frac{6}{2} = 3 \]

2. **Calculate the y-coordinate of S:**
\[ y = \frac{y_1 + y_2}{2} = \frac{7 + 1}{2} \]
\[ y = \frac{8}{2} = 4 \]

### Step 3: Write the coordinates of S
Thus, the coordinates of point S are \( (3, 4) \).

### Final Answer
The coordinates of S are \( (3, 4) \).

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