A point P lies on x-axis and another point Q lies on y-axis.
If the abscissa of the point P is -12 and the ordinate of the point Q is -16, calculate the length of the segment PQ.

Answer

To find the length of the segment \( PQ \) where point \( P \) lies on the x-axis and point \( Q \) lies on the y-axis, we will follow these steps:

1. **Identify the coordinates of point P and point Q**:
- Since point \( P \) lies on the x-axis and its abscissa (x-coordinate) is -12, the coordinates of point \( P \) are \( (-12, 0) \).
- Since point \( Q \) lies on the y-axis and its ordinate (y-coordinate) is -16, the coordinates of point \( Q \) are \( (0, -16) \).

2. **Use the distance formula**:
The distance \( d \) between two points \( (x_1, y_1) \) and \( (x_2, y_2) \) is given by the formula:
\[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \]
Here, we will let \( P = (x_1, y_1) = (-12, 0) \) and \( Q = (x_2, y_2) = (0, -16) \).

3. **Substitute the coordinates into the distance formula**:
\[ d = \sqrt{(0 - (-12))^2 + (-16 - 0)^2} \]
Simplifying this gives:
\[ d = \sqrt{(0 + 12)^2 + (-16)^2} \]
\[ d = \sqrt{12^2 + 16^2} \]

4. **Calculate the squares**:
\[ d = \sqrt{144 + 256} \]

5. **Add the squares**:
\[ d = \sqrt{400} \]

6. **Take the square root**:
\[ d = 20 \]

Thus, the length of the segment \( PQ \) is \( 20 \) units.