Question

What is the image point of (4,0) after the transformation T-1,20 R90?

Answer 1

The image of the point after the transformation is (2,-3)

Here, we want to get the image of the point after translation, followed by rotation

When we translate, we move some units up and below the axes

With the given relation, we are going to move 1 units vertically, and 2 units horizontally

This means that we are to add 1 to the vertical axis and 2 to the horizontal axis

We have this as;

$(4-1,\text{ 0+2) = (3,2)}$

what is left is the rotation by 90 degrees

Given the pre-image (x,y); after 90 degrees clockwise rotation, we are going to have the coordinates as (y,-x)

Thus, what we have after rotation is (2,-3)