Question

(–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)

Answer 1

Answer: 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.

Answer 2

A. (0, –1)

Explanation:

Let the point representing the pre-image = (x,y)

So, we have,

`T_(-2,4)\circ R_(x-axis)(x,y)=(-2,-3)`

So, to find the co-ordinates (x,y), we will go reverse form the point (-2,-3).

Reflection around x-axis of (-2,-3) is (-2,3).

Since, we are applying,

Translation of 2 units to the left and 4 units up to the point (x,y).

So, we will apply,

Translation of 2 units to the right and 4 units down to the point (-2,3).

So, the translated point is (-2+2,3-4) = (0,-1).

Hence, the co-ordinates of the pre-image is (0,-1).