Question

Apply the transformation (x, y) --> (1/2x, 1/2y) to 'PQR. What are the new Coordinates for P', Q', R'? Describe what happened to the preimage.

Options:
a. P'(0, 0), Q'(1, 2), R'(3, 4); The preimage was shrunk by a factor of 2 in both x and y.
b. P'(2, 4), Q'(4, 8), R'(6, 12); The preimage was enlarged by a factor of 2 in both x and y.
c. P'(0, 0), Q'(2, 4), R'(4, 8); The preimage was shifted to the right and upwards.
d. P'(1/2, 1/2), Q'(1, 2), R'(3/2, 3/2); The preimage was compressed towards the origin.

Answer 1

To find the new coordinates for P', Q', and R', we simply multiply each coordinate of PQR by 1/2. The preimage was shrunk by a factor of 2 in both the x and y directions. The correct option is: d. P'(1/2, 1/2), Q'(1, 2), R'(3/2, 3/2); The preimage was compressed towards the origin.

Step-by-step explanation:

The correct option is: d. P'(1/2, 1/2), Q'(1, 2), R'(3/2, 3/2); The preimage was compressed towards the origin.

When the transformation (x, y) → (1/2x, 1/2y) is applied to points P, Q, and R, the x-coordinates and y-coordinates are halved. This results in a compression of the preimage towards the origin, as each coordinate is reduced by a factor of 2.

For example:

- P(1, 1) becomes P'(1/2, 1/2),

- Q(2, 4) becomes Q'(1, 2),

- R(3, 6) becomes R'(3/2, 3/2).

This transformation is a type of scaling, where the preimage is compressed in both the x and y directions by a factor of 2.