The length of the foot of perpendicular drawn from
the point P(3, 6, 7) on y-axis is

Options

A. `sqrt(48)`
B. `sqrt(45)`
C. 3
D. `sqrt(58)`

Answer

To find the length of the foot of the perpendicular drawn from the point P(3, 6, 7) to the y-axis, we can follow these steps:

### Step 1: Understand the coordinates
The point P has coordinates (3, 6, 7). Here, the x-coordinate is 3, the y-coordinate is 6, and the z-coordinate is 7.

### Step 2: Identify the foot of the perpendicular on the y-axis
The foot of the perpendicular from a point to the y-axis will have the same y-coordinate as the point but will have the x and z coordinates as zero. Therefore, the foot of the perpendicular from P(3, 6, 7) to the y-axis is (0, 6, 0).

### Step 3: Calculate the length of the perpendicular
The length of the perpendicular from point P to the y-axis can be calculated using the formula:
\[ \text{Length} = \sqrt{(x_1 - x_2)^2 + (z_1 - z_2)^2} \]
where (x1, y1, z1) are the coordinates of point P and (x2, y2, z2) are the coordinates of the foot of the perpendicular on the y-axis.

Here,
- \( (x_1, y_1, z_1) = (3, 6, 7) \)
- \( (x_2, y_2, z_2) = (0, 6, 0) \)

Substituting the values:
\[ \text{Length} = \sqrt{(3 - 0)^2 + (7 - 0)^2} \]
\[ = \sqrt{3^2 + 7^2} \]
\[ = \sqrt{9 + 49} \]
\[ = \sqrt{58} \]

### Step 4: Conclusion
Thus, the length of the foot of the perpendicular drawn from the point P(3, 6, 7) on the y-axis is \(\sqrt{58}\) units.

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