(–2, –3) is the image produced by applying the composition t -2.4 rx to a point. what are the coordinates of the preimage?

a.
(0, –1)
b.
(0, 1)
c.
(3, 4)
d.
(0, 7)

Hello mate!

The composition T(-2.4)oRx means a translation of -2 units in x and 4 units in y, and a reflection over the x-axis.

We know that after this composition, our pair is (-2, -3) and we want to find the initial pair.

For doing this we need to apply the inverse composition:

The inverse of R(x) is R(x) (if you reflect a point two times over the same axis, you return to the same position)

and the inverse of T(-2,4) is T(2,-4)

this means that to return to the original point, we need to apply:

R(x)T(2,-4) to the pair (-2, -3)

Notice tath in the first part we apply the rotation first and the translation after, this means that now we need to cancel the translation first, and then cancel the rotation; then we apply the inverse translation first:

T(2,-4)(-2, -3) = (2 - 2, -3 - 4) = (0,-7)

now we apply the rotation, wich leaves the x part unperturbed and changes the sign in the y part.

R(x)(0,-7) = (0, 7)

then the right option is D.

true

explanation: