The point (1,13)

Question

lies on the line f(x)=13x
. The function g(x)=log13x
includes a point of a reflection across the line y=x
that lies on the line g(x)=log13x
. In which quadrant of the coordinate plane is this point located?(1 point)
Responses

Quadrant I
Quadrant I

Quadrant II
Quadrant II

Quadrant IV
Quadrant IV

Quadrant III
Quadrant III

Answer 1

To determine the quadrant of the point that results from reflecting the point \((1, 13)\) across the line \(y = x\), we first find the reflection of that point.

The reflection of a point \((a, b)\) across the line \(y = x\) is given by the point \((b, a)\). Therefore, the reflection of the point \((1, 13)\) is \((13, 1)\).

Next, we need to identify which quadrant this new point, \((13, 1)\), is located in:

• In the coordinate plane:
  • Quadrant I: \(x > 0\) and \(y > 0\)
  • Quadrant II: \(x < 0\) and \(y > 0\)
  • Quadrant III: \(x < 0\) and \(y < 0\)
  • Quadrant IV: \(x > 0\) and \(y < 0\)

Since both \(x = 13\) and \(y = 1\) are greater than 0, the point \((13, 1)\) is located in Quadrant I.

Therefore, the answer is:

Quadrant I