Question

Match each description to its example.

1. (2, -3) → (-3, 2) reflection across both axes
2. (2, -3) → (2, 3) reflection across the x-axis
3. (2, -3) → (-2, -3) not a reflection
4. (2, -3) → (-2, 3) reflection across the y-axis

Answer 1

To match each description to its example, we need to analyze the reflection across the axes and identify the changes in coordinates.

Step-by-step explanation:

To match each description to its example, let's analyze each option:

1. (2, -3) → (-3, 2): This is a reflection across both axes, meaning that both the x-coordinate and y-coordinate are negated. So, the answer is 1.
2. (2, -3) → (2, 3): This is a reflection across the x-axis, which means that only the y-coordinate is negated. So, the answer is 2.
3. (2, -3) → (-2, -3): This is not a reflection because the coordinates do not change. So, the answer is 3.
4. (2, -3) → (-2, 3): This is a reflection across the y-axis, which means that only the x-coordinate is negated. So, the answer is 4.

Answer 2

(2, -3) → (2, 3) reflection across the x-axis

(2, -3) → (-2, -3) reflection across the y-axis

(2, -3) → (-2, 3) reflection across both axes

(2, -3) → (-3, 2) not a reflection

Step-by-step explanation:

Reflection across the x-axis:

When we reflect a point across the x-axis, it's x coordinate keeps the same value, while the signal of the y-coordinate is changed, having the same value, with different signal.

So the correct option is:

(2, -3) → (2, 3) reflection across the x-axis

Reflection across the y-axis:

When we reflect a point across the y-axis, it's y coordinate keeps the same value, while the signal of the x-coordinate is changed, having the same value, with different signal.

So the correct option is:

(2, -3) → (-2, -3) reflection across the y-axis

Reflection across both axis:

Both change the signal. So

(2, -3) → (-2, 3) reflection across both axes

Rotations:

When we have a rotation, not only the signals can change, but also the numbers, x with y and y with x. Rotations are not reflections. So

(2, -3) → (-3, 2) not a reflection