Suppose you start at the origin, move along the x-axis a distance of 7 units in the positive direction, and then move downward along the z-axis a distance of 5 units. What are the coordinates of your position?
(x, y, z) =

Starting at the origin, the coordinates are \((0, 0, 0)\).

- First, you move along the x-axis 7 units in the positive direction, so the new coordinates will be \((7, 0, 0)\), as the y and z coordinates remain unchanged.
- Then, you move downward 5 units along the z-axis, which means you subtract 5 from the z-coordinate. The new coordinates become \((7, 0, -5)\).

Thus, the final coordinates of your position are:
\[
(x, y, z) = (7, 0, -5)
\]

Would you like more details or have any questions?

Here are 5 related questions:
1. What are the coordinates if you move 3 units along the y-axis instead of the z-axis?
2. How would the coordinates change if you moved 7 units along the negative x-axis?
3. What is the distance from the origin to the final point \((7, 0, -5)\)?
4. If you moved upward 8 units along the z-axis instead of downward, what would the coordinates be?
5. What is the result if you moved 7 units along both the x-axis and y-axis?

**Tip:** To calculate distance between two points in 3D space, use the distance formula \(d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2 + (z_2 - z_1)^2}\).

Explore how coordinates change after moving 7 units along the x-axis and 5 units downward along the z-axis. Learn using the distance formula in 3D space. Suitable for students in Grades 6-8.

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