Question

The point (1,13) lies on the line f(x)=13^x

. The function g(x)=log base 13 x includes a point that is a reflection across the line y=x that lies on the line g(x) = log base 13 x. In which quadrant of the coordinate plane is this point located?

Answer 1

To determine the reflection of the point (1, 13) across the line \( y = x \) and identify in which quadrant it lies, we first understand how reflection across the line \( y = x \) works.

When a point \( (a, b) \) is reflected across the line \( y = x \), the coordinates of the reflected point become \( (b, a) \).

For the point \( (1, 13) \):
- The reflection across the line \( y = x \) gives us the point \( (13, 1) \).

Now we need to identify the quadrant in which the point \( (13, 1) \) lies.

- The x-coordinate is 13, which is positive.
- The y-coordinate is 1, which is also positive.

Since both coordinates are positive, the point \( (13, 1) \) lies in the **first quadrant** of the coordinate plane.

Thus, the answer is that the reflected point is located in the **first quadrant**.