P (5, -1) and Q (5, 10) lie on a straight line.The following are a few statements concerning these points on the line. I.      The gradient of the straight line is undefined.II.     The gradient of the straight line is zero.III.    (-5, 8) lies on the straight line. Which of the following statement(s) is/are true?

The gradient of a line is calculated by the formula (y2 - y1) / (x2 - x1).

I. The gradient of the straight line is undefined. To check this, we substitute the given points into the formula. The x-coordinates of both points are the same (5), so the denominator of the formula becomes zero (5 - 5 = 0). Since division by zero is undefined in mathematics, the gradient of the line is indeed undefined. So, statement I is true.

II. The gradient of the straight line is zero. This statement is false. A line has a zero gradient if it is horizontal, meaning all y-coordinates of the points on the line are the same. In this case, the y-coordinates of points P and Q are different (-1 and 10), so the line is not horizontal and the gradient is not zero.

III. (-5, 8) lies on the straight line. Since the x-coordinate of this point is different from the x-coordinates of points P and Q, this point does not lie on the same vertical line. So, statement III is false.

In conclusion, only statement I is true.