Question

the point (4, 3, - 2) is represented by which graph below? look closely at the z - axis.

Explanation:

Step1: Analyze the coordinates

The point is \((4,3, - 2)\). In a 3 - D coordinate system \((x,y,z)\), \(x = 4\) (positive \(x\) - direction), \(y = 3\) (positive \(y\) - direction), \(z=-2\) (negative \(z\) - direction).

Step2: Check each graph

• Graph A: The \(z\) - coordinate is positive (point is above the \(xy\) - plane).
• Graph B: The \(z\) - coordinate is positive (point is above the \(xy\) - plane).
• Graph C: The \(x\) and \(y\) coordinates are positive, but the path shown does not correspond to the correct \(z\) - value.
• Graph D: Move \(4\) units along the \(x\) - axis, \(3\) units along the \(y\) - axis, and \(2\) units down (negative \(z\) - axis).

Answer:

D