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a point located at (5, -2) undergoes two transformations. its image is located at (-5, 2). what were the transformations?

the point was reflected over the y -axis and translated up 4 units.
the point was translated right 10 units and reflected over the x -axis.
the point was translated left 10 units and up 4 units.
the point was reflected over the y -axis and translated down 4 units.

#1 : reflected over y-axis, so x changes signs and becomes negative (-5, -2)

translated 4 units up, so move the point up 4 units/squares  (-5, 2)

#2 translated right 10 units, so the points move right 10 squares (15, -2)

reflected over x-axis, so y changes signs (15, -2)

#3 translated left 10 units (-5, -2)

up 4 units (-5, 2)

#4 reflected over the y -axis (-5, -2)

translated down 4 units (-5, -6)

x = ± 6i

step-by-step explanation:

x^2 = -36

take the square root of each side

sqrt(x^2) = sqrt(-36)

we know sqrt(ab) = sqrt(a) sqrt(b)

x = ±sqrt(36) sqrt(-1)

we know that sqrt (-1) = i

x = ± 6i