Let's work through the questions in the image you've uploaded. Here's a breakdown of the problems:

Problem 6:

Reflection of point G(5, 3) over the x-axis:

When a point is reflected over the x-axis, the y-coordinate changes sign while the x-coordinate remains the same. So the coordinates of the reflected point $G'$ will be: $G'(5, -3)$

Problem 7:

Reflection of point T(1, 6) over the line $y = x$:

When reflecting a point over the line $y = x$, the x- and y-coordinates are swapped. So the coordinates of the reflected point $T'$ will be: $T'(6, 1)$

Problem 8:

This problem asks you to write a reflection rule for mapping each triangle to its image:

Part (a):

Points are given as $J(1, 0), K(-5, 2), L(4, -4)$, and their corresponding reflected points $J'(-9, 0), K'(-5, -2), L'(4, 4)$.

By examining the changes in the coordinates:

• For $J$ to $J'$, the reflection occurs over the line $x = -4$.
• For $K$ to $K'$, the y-coordinate changes sign, which is a reflection over the x-axis.
• For $L$ to $L'$, the y-coordinate also changes sign.

So the reflection seems to be over the x-axis.

Part (b):

Points are given as $P(8, 6), Q(-4, 12), R(7, 7)$, and their corresponding reflected points $P'(8, -20), Q'(-4, -12), R'(7, -7)$.

Here, it seems that the reflection is happening over the x-axis again, since all the y-coordinates are changing sign.

Would you like further details or clarification on any of these steps?

Relative Questions:

1. How would the reflection of a point over the y-axis change the coordinates?
2. How do you reflect a point over a diagonal line like $y = -x$?
3. What are the properties of a rigid transformation, and why is a size change not a rigid motion?
4. Could you reflect a figure over an arbitrary line, like $y = 2x + 1$? How would you do it?
5. How can you determine whether a transformation is a rotation or reflection based only on the coordinates?

Tip:

For reflections over the x-axis or y-axis, remember to only change the sign of one coordinate: the y-coordinate for reflections over the x-axis and the x-coordinate for reflections over the y-axis.