Question

Point A is at `(3 ,2 )` and point B is at `(-7 ,3 )`. Point A is rotated `pi/2` clockwise about the origin. What are the new coordinates of point A and by how much has the distance between points A and B changed?

Answer 1

Rotating Point A `(3, 2)` clockwise through `pi/2` yields Point A' `(2, -3)`. We can then calculate the distance between Point A' and Point B as approximately `10.8` `units`.

Explanation:

Now, `pi/2` is `1/4` of a full rotation (`2pi`) or `90^o`. If we rotate the point `(3, 2)` through this angle clockwise, we move from the first to the fourth quadrant, so the `x` value will still be positive and the `y` value will be negative.

You should probably draw a diagram, but it turns out that the new point, which we can call Point A', has the coordinates `(2, -3)`.

We can calculate the distance between Point A' and Point B:

`r=sqrt((x_2-x_1)^2+(y_2-y_1)^2)=sqrt(((-7)-2)^2+(3-(-3))^2)=sqrt(81+36)~~10.8`