Just using geometry:

Form a right triangle by dropping a line from point (6.9) down to (6,-6) and a line from (-4,-6) to (6,-6).

Let A = (6,9)

Let B = (-4,-6), and

Let C = (6,-6)

Line AC has a length of 15 and line BC has a length of 10.

Calculate the tangent of angle ∠ABC. Opposite over adjacent.

Create a triangle ΔDEF that is congruent to ΔABC with the given point (-3,2) as point E of the new triangle and side DE parallel to side AB. Extend the line DE out in each direction. The answer must lie on this line.

At this point I would plot all four answers. One of these will fall on the extended line DE.

Check it by comparing the difference between the y's of the answer and point (-3,2) divided by the difference of the x's of the answer and point (-3,2). That should be equal to the tangent calculated.

Answer C (3,11) lies on the line DE.

To check take (11-2)/(3-(-3)) = 9/6 = 3/2.

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