Question

Let a, and define by . Find the images under t of and .

Answer 1

The images of the points (1, 4) and (-3, 0) under the transformation t are (3, 1) and (-1, -3) respectively.

Step-by-step explanation:

For a transformation t defined as t(x, y) = (x + 2, y - 3), applying this transformation to the point (1, 4) involves adding 2 to the x-coordinate and subtracting 3 from the y-coordinate, resulting in (1 + 2, 4 - 3) = (3, 1). Similarly, for the point (-3, 0), adding 2 to the x-coordinate and subtracting 3 from the y-coordinate gives (-3 + 2, 0 - 3) = (-1, -3).

This transformation shifts each point by (+2) units in the x-direction and (-3) units in the y-direction. So, the images of the given points (1, 4) and (-3, 0) under the transformation t are accordingly transformed to (3, 1) and (-1, -3).

Here is complete question;

"Let t be a transformation,
`\(t: \mathbb{R}^2 \rightarrow \mathbb{R}^2\),` defined by t(x, y) = (x + 2, y - 3).

Find the images under t of the points (1, 4) and (-3, 0)."