In the *x**y*-plane, the line determined by the points (9, k) and* (k*, 9) passes through the origin.

Which of the following could be the value of *k*?

A) 0

B) 3

C) 9

D) 81

Solution:

**Choice C is correct.**

We are being given that the line passes through the points (9,k), *(k*,9), (0,0)

Since the line passes through (0,0) and (9,k), the slope of the line is given by (k-0) / (9-0) = k/9.

Similarly, since the line passes through (0, 0) and (k, 9), the slope of the line is given by (9-0) / (k-0) = 9/k.

As we are taking about the same lines, the slopes should be equal.

Therefore k/9 = 9/k

or K ^{2}=81

Hence, k = +9 or k = -9.

Therefore from the choices provided, only 9 could be the value of k.

Note: If you notice the question closely, the question states, which of
the following **could be** the value of *k*?

The word “could be” implies more than one value might be possible for k.