Question

1. when point f ( , ) is reflected in the line y = x, the image is located at f (-7, 1).

Explanation:

Step1: Recall Reflection over \( y = x \)

When a point \((a, b)\) is reflected over the line \( y = x \), the coordinates of the image are \((b, a)\). This is because the line \( y = x \) swaps the \( x \)- and \( y \)-coordinates of a point.

Step2: Apply the Reflection Rule

We know the image after reflection over \( y = x \) is \( F'(-7, 1) \). Let the original point be \( F(x, y) \). Using the reflection rule, if the image is \((b, a)\) when the original is \((a, b)\), then for the image \((-7, 1)\), the original point \( F \) must have coordinates \((1, -7)\). Because we swap the \( x \)- and \( y \)-coordinates of the image to get the original point.

Answer:

The original point \( F \) has coordinates \((1, -7)\), so the first blank (x - coordinate) is \( 1 \) and the second blank (y - coordinate) is \( -7 \).