Question

What is the distance of the point \((1,2,3)\) from the \(yz\)-plane?

• A. \(3\)
• B. \(2\)
• C. \(1\)
• D. \(\sqrt{3}\)

Hint:

Distance from coordinate planes: \[ \text{Distance from } yz\text{-plane} = |x|,\quad \text{from } xz\text{-plane} = |y|,\quad \text{from } xy\text{-plane} = |z|. \]

Answer 1

The Correct Option is C

Topic - Three Dimensional Geometry (Coordinates):
This question deals with the concept of coordinate planes and how to calculate the distance of a point from them.
Step 1: Understanding the Question:
We are given a point \(P(1, 2, 3)\) and need to find how far it is from the \(yz\)-plane.
Step 2: Key Formula or Approach:
The equation of the \(yz\)-plane is \(x = 0\).
The perpendicular distance of a point \((x_1, y_1, z_1)\) from:
- \(yz\)-plane is \(|x_1|\).
- \(xz\)-plane is \(|y_1|\).
- \(xy\)-plane is \(|z_1|\).
Step 3: Detailed Solution:
1. Identify the coordinates of the point: \(x = 1, y = 2, z = 3\).
2. To find the distance from the \(yz\)-plane, we look at the absolute value of the \(x\)-coordinate.
3. Distance = \(|1| = 1\).
Step 4: Final Answer:
The distance is 1 unit.