The image of the point (-2, 3, 4) by reflection in the z-axis is ...

a) (-2, 3, 4)

b) (2, 3, 4)

c) (2,-3,-4)

d) (2, -3, 4)

To find the image of the point \((-2, 3, 4)\) by reflection in the \(z\)-axis, we keep the \(z\) coordinate the same and change the sign of the \(x\) coordinate. The \(y\) coordinate remains unchanged.

So, the reflection in the \(z\)-axis transforms \((-2, 3, 4)\) as follows:

- \(x\) changes from \(-2\) to \(2\)
- \(y\) remains \(3\)
- \(z\) remains \(4\)

Thus, the reflected point is \((2, 3, 4)\).

The correct answer is **b) (2, 3, 4)**.

Do you want details or have any questions? Here are some related questions you might find interesting:

1. How would the reflection change if we reflected in the \(x\)-axis instead?
2. What is the general formula for reflecting a point in a given axis in 3D?
3. Can you describe how to visualize reflections in three-dimensional space?
4. What is the effect of multiple reflections in different axes on a point?
5. How do reflections relate to transformations in geometry?

**Tip:** When reflecting points in space, always remember which axis you are reflecting across, as it affects the coordinates differently.

The image of the point (-2, 3, 4) by reflection in the z-axis is ...

Explore how to find the image of the point (-2, 3, 4) by reflection in the z-axis. The transformation keeps the z-coordinate the same while changing the sign of the x-coordinate, resulting in the point (2, 3, 4). Ideal for students in Grades 6-8 learning about geometry and reflections.

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