Question

For the transformation T, write the T-1.

T: (x, y) ( 2x, y + 5)
T -1 (x, y)

(x - 2, y - 5)
(½x, y - 5)
(2x - 1, y + 4)

Answer 1

Answer: Choice B) (1/2x, y - 5)

The original transformation T takes some point (x,y) and turns it into (2x, y+5). What's going on with the coordinates? Well x is doubled to 2x while y is having 5 added to it. To get the inverse, we simply undo everything happening to the coordinates. We do the opposite.

Going from x to 2x has us multiply by 2. To backwards, we divide by 2. This is the same as multiplying by 1/2. At this point, the only answer is B. So we could stop here if we wanted. But let's keep going.

To go from y to y+5, we add on 5. Undo this by subtracting 5. So the inverse would be y-5.

That's why the inverse transformation is (1/2x, y-5)