In the xy-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.