Question

Find the distance of the point \( (1,-2,3) \) from the \(yz\)-plane.

• A. \(0\)
• B. \(1\)
• C. \(2\)
• D. \(3\)

Hint:

For coordinate planes: Distance from \(yz\)-plane \(= |x|\) Distance from \(xz\)-plane \(= |y|\) Distance from \(xy\)-plane \(= |z|\)

Answer 1

The Correct Option is B

Topic: Three-Dimensional Geometry
Step 1: Understanding the Question:
The question asks for the perpendicular distance of a specific point in 3D space from one of the primary coordinate planes, specifically the \(yz\)-plane.
Step 2: Key Formula or Approach:
The distance of any point \(P(x, y, z)\) from the coordinate planes is given by:
1. Distance from \(yz\)-plane (\(x=0\)) is \(|x|\).
2. Distance from \(xz\)-plane (\(y=0\)) is \(|y|\).
3. Distance from \(xy\)-plane (\(z=0\)) is \(|z|\).
Step 3: Detailed Explanation:
The given point is \(P(1, -2, 3)\).
Here, the \(x\)-coordinate is 1, the \(y\)-coordinate is \(-2\), and the \(z\)-coordinate is 3.
To find the distance from the \(yz\)-plane, we look at the absolute value of the \(x\)-coordinate.
\[ \text{Distance} = |1| = 1 \]
Step 4: Final Answer:
The distance of the point from the \(yz\)-plane is 1 unit.