What is the distance of the point `(1,2,0)` from YZ plane is

Options

A. 1 unit
B. 2 unit
C. 3 unit
D. 4 unit

Answer

To find the distance of the point \((1, 2, 0)\) from the YZ plane, we can follow these steps:

### Step 1: Understand the YZ Plane
The YZ plane is defined by the equation \(x = 0\). This means that any point on the YZ plane has an x-coordinate of 0.

### Step 2: Identify the Coordinates of the Given Point
The given point is \((1, 2, 0)\). Here, the coordinates are:
- \(x_1 = 1\)
- \(y_1 = 2\)
- \(z_1 = 0\)

### Step 3: Use the Distance Formula
The distance \(d\) from a point \((x_1, y_1, z_1)\) to a plane given by the equation \(ax + by + cz + d = 0\) can be calculated using the formula:

\[ d = \frac{|ax_1 + by_1 + cz_1 + d|}{\sqrt{a^2 + b^2 + c^2}} \]

### Step 4: Determine the Plane Equation
For the YZ plane, the equation can be expressed as:
\[ x = 0 \quad \text{or} \quad 1x + 0y + 0z + 0 = 0 \]
This means:
- \(a = 1\)
- \(b = 0\)
- \(c = 0\)
- \(d = 0\)

### Step 5: Substitute Values into the Distance Formula
Now we substitute the values into the distance formula:
\[ d = \frac{|1 \cdot 1 + 0 \cdot 2 + 0 \cdot 0 + 0|}{\sqrt{1^2 + 0^2 + 0^2}} \]

### Step 6: Simplify the Expression
Calculating the numerator:
\[ d = \frac{|1 + 0 + 0 + 0|}{\sqrt{1}} = \frac{|1|}{1} = 1 \]

### Step 7: Conclusion
The distance of the point \((1, 2, 0)\) from the YZ plane is \(1\) unit.

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