What are the coordinates of the mid-point of (2a, 0) and (0, 2b).

Options

A. (a, b)
B. (a, 2)
C. (b, a)
D. (2, b)

Answer

To find the coordinates of the midpoint of the points (2a, 0) and (0, 2b), we can follow these steps:

### Step 1: Identify the coordinates of the points
We have two points:
- Point A: (2a, 0)
- Point B: (0, 2b)

### Step 2: Use the midpoint formula
The formula for finding the midpoint \( M \) of two points \( (x_1, y_1) \) and \( (x_2, y_2) \) is given by:
\[ M = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right) \]
Here, \( (x_1, y_1) = (2a, 0) \) and \( (x_2, y_2) = (0, 2b) \).

### Step 3: Substitute the coordinates into the formula
Now, substituting the coordinates into the midpoint formula:
\[ M = \left( \frac{2a + 0}{2}, \frac{0 + 2b}{2} \right) \]

### Step 4: Simplify the expressions
Now, simplify each component:
- For the x-coordinate:
\[ \frac{2a + 0}{2} = \frac{2a}{2} = a \]
- For the y-coordinate:
\[ \frac{0 + 2b}{2} = \frac{2b}{2} = b \]

### Step 5: Write the final coordinates of the midpoint
Thus, the coordinates of the midpoint \( M \) are:
\[ M = (a, b) \]

### Final Answer
The coordinates of the midpoint of the points (2a, 0) and (0, 2b) are \( (a, b) \).

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