Answer
$q_1$ is positive
Work Step by Step
On the graph, we can see that when particle 3 is at $x = 2.0~cm$, the forces on particle 3 due to the other two particles have the same magnitude.
When $x \lt 2.0~cm$, the magnitude of the force on particle 3 due to particle 1 is greater than the magnitude of the force on particle 3 due to particle 2. When $x \lt 2.0~cm$, the net force on particle 3 is in the positive x direction.
Then the force on particle 3 due to particle 1 is in the positive x direction.
Therefore, $q_1$ is positive, since it is given in the question that $q_3$ is positive.
