You are right about they being negative reciprocals.
But the definition of a reciprocal is: "A mathematical expression or function so related to another that their product is one; the quantity obtained by dividing the number one by a given quantity."
Which means [tex] \frac{1}{3} [/tex] is the reciprocal of 3 because when you multiply them you get 1.
Negative reciprocals means, on the other hand, literally negative of reciprocals.
For example, [tex] - \frac{1}{3} [/tex] is the negative reciprocal of 3.
And when you multiply a number with its negative reciprocal, you get -1.
In choices, it says "the product of", which means when you multiply two numbers, the answer is the product of the two numbers.
So, if their slopes are negative reciprocals, their "product" has to be -1.
