A software engineer uses perspective projection in AR, where a point $(x, y, z)$ with $z > 0$ projects to $(x/z, y/z, 0)$ on the screen. If a virtual object at $(8, 6, 4)$ is viewed, and the screen is at $z = 2$, what is the projected 2D coordinate?

["Title: How Perspective Projection Transforms 3D AR Coordinates to Screen Space", "In augmented reality (AR) applications, transforming 3D world coordinates into a 2D screen display requires a fundamental technique called perspective projection. This process simulates how objects appear smaller as they recede into the distance—just as how a mountain fades and shrinks in the distance when viewed from afar.", "Perspective projection maps a 3D point $(x, y, z)$ with $z > 0$ to a 2D screen coordinate by scaling the $x$ and $y$ values inversely to depth $z$. Specifically, a point $(x, y, z)$ projects to a 2D screen position of $\left( \frac{x}{z},\ \frac{y}{z},\ 0 \right)$, placing the object within the virtual camera’s view frustum aligned to the screen plane.", "### Example: Virtual Object at (8, 6, 4) Projected on a Screen at $z = 2$", "Let’s apply the projection formula to the point $(x, y, z) = (8, 6, 4)$, where the screen is located at $z = 2$.", "Compute the projected 2D coordinates:\n$$\nx' = \frac{x}{z} = \frac{8}{4} = 2\n$$\n$$\ny' = \frac{y}{z} = \frac{6}{4} = 1.5\n$$", "So, the virtual object at 3D coordinates $(8, 6, 4)$ is projected onto the 2D screen at position $(2, 1.5)$.", "This计算 not only demonstrates the mechanics of perspective projection but also shows how AR systems accurately place distant virtual objects closer to the edge of the screen—mimicking natural human depth perception and enhancing immersion.", "In summary:\nFor a 3D point $(8, 6, 4)$ viewed through a plane at $z = 2$, the projected 2D coordinate is $(2, 1.5)$. This is a core concept in AR development, forming the foundation for realistic and spatially accurate augmented experiences.", "---", "Keywords: perspective projection, AR coordinate transformation, 3D to 2D projection, point (x, y, z) projection, augmented reality calibration, depth mapping, screen space projection."]