A line is such that its segment between the axes is bisected at the point (23, 27) the product of the intercepts made by the line on the coordinate axes is.

Answer

To solve the problem, we need to find the product of the intercepts made by the line on the coordinate axes, given that the segment of the line between the axes is bisected at the point (23, 27).

### Step-by-step Solution:

1. **Understanding the Intercepts**:
Let the x-intercept of the line be \( A \) and the y-intercept be \( B \). The coordinates of the x-intercept are \( (A, 0) \) and the coordinates of the y-intercept are \( (0, B) \).

2. **Equation of the Line**:
The equation of the line in intercept form is given by:
\[ \frac{x}{A} + \frac{y}{B} = 1 \]

3. **Finding the Midpoint**:
The midpoint of the segment between the x-intercept and y-intercept can be calculated using the midpoint formula:
\[ \text{Midpoint} = \left( \frac{A + 0}{2}, \frac{0 + B}{2} \right) = \left( \frac{A}{2}, \frac{B}{2} \right) \]
According to the problem, this midpoint is given as \( (23, 27) \).

4. **Setting Up the Equations**:
From the midpoint coordinates, we can set up the following equations:
\[ \frac{A}{2} = 23 \quad \text{(1)} \]
\[ \frac{B}{2} = 27 \quad \text{(2)} \]

5. **Solving for A and B**:
From equation (1):
\[ A = 2 \times 23 = 46 \]
From equation (2):
\[ B = 2 \times 27 = 54 \]

6. **Calculating the Product of the Intercepts**:
Now, we need to find the product \( AB \):
\[ AB = 46 \times 54 \]

7. **Performing the Multiplication**:
To calculate \( 46 \times 54 \):
\[ 46 \times 54 = 2484 \]

8. **Final Answer**:
Thus, the product of the intercepts made by the line on the coordinate axes is:
\[ \boxed{2484} \]