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

Answer

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

### Step 1: Identify the coordinates of points P and Q.
- Point P lies on the x-axis, and its abscissa (x-coordinate) is -12. Therefore, the coordinates of point P are (-12, 0).
- Point Q lies on the y-axis, and its ordinate (y-coordinate) is -16. Therefore, the coordinates of point Q are (0, -16).

### Step 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:
\[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \]

### Step 3: Assign the coordinates to the formula.
Let:
- \(P = (x_1, y_1) = (-12, 0)\)
- \(Q = (x_2, y_2) = (0, -16)\)

Now substituting the coordinates into the distance formula:
\[ d = \sqrt{(0 - (-12))^2 + (-16 - 0)^2} \]

### Step 4: Simplify the expression.
Calculating the differences:
\[ d = \sqrt{(0 + 12)^2 + (-16)^2} \]
\[ d = \sqrt{(12)^2 + (-16)^2} \]

### Step 5: Calculate the squares.
Calculating the squares:
\[ d = \sqrt{144 + 256} \]

### Step 6: Add the squares.
Adding the squares:
\[ d = \sqrt{400} \]

### Step 7: Take the square root.
Taking the square root of 400:
\[ d = 20 \]

### Conclusion:
The length of the line segment PQ is 20 units.

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