Question

The Cartesian equation of the plane passing through the point $A(7, 8, 6)$ and parallel to the XY plane is

• A. $z = 1$
• B. $y = 8$
• C. $x = 7$
• D. $z = 6$

Hint:

This is a visual shortcut question! A plane parallel to the XY plane locks the Z value. A plane parallel to the YZ plane locks the X value. A plane parallel to the XZ plane locks the Y value. Just grab the corresponding coordinate from the given point!

Answer 1

The Correct Option is D

Step 1: Recall the XY plane.
Every point on the XY plane has height zero, so the XY plane is $z=0$.
Step 2: Think about a parallel plane.
A plane parallel to the XY plane keeps the same height everywhere, so it must be $z=c$ for some constant $c$.
Step 3: Use the given point.
The plane passes through $A(7,8,6)$, so the height there is $z=6$.
Step 4: Fix the constant.
Therefore $c=6$, and the plane is $z=6$.
Step 5: Confirm the other coordinates do not matter.
Being parallel to XY means $x$ and $y$ are free; only the $z$ value is fixed.
Step 6: State the answer.
The equation is $z=6$, which is option (4). \[ \boxed{z=6} \]