Question seems complicated, but is not.

But let point A be (-3,b). The given line has gradient -(2/5). Therefore gradient of AB is 5/2.

Since B is (3,5), gradient of AB being (5-b)/(3+3) = 5/2. It follows b = -10

i.e the required point A is (-3,-10)

Silove's solution rather long-winded and is harder than necessary. You don't need the equation of AB.

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