Atriangle is rotated 90° about the origin. which rule describes the transformation?

Here's what your typical x any y axis look like. (Picture 1)

Now here's what they look like rotated 90 degrees. (Picture 2)

When we rotate the axes by 90 degrees, we rotate every point in the coordinate plane by 90, too, so if we look at how the axes have been transformed, we can describe the transformation of every point, too.

We notice that, where the y-axis used to be, we now have the x axis, so every point is going to have its x coordinate swapped to the y coordinate in the rotation - for example, a point with the coordinate (1, 0) will have the transformed coordinate (0, 1).

What else happens to the axes? The y-axis seems to take the place of the x-axis, but it also gets flipped in the rotation. Every y-coordinate is going to get swapped to the x-coordinate, but they'll also be multiplied by -1 to account for the "flipping". The general rule then is "flip the sign of the y-coordinate, swap the coordinates." Symbolically, we'd say that, for every point P and its transformed point P':

P(x, y) ⇒ P'(-y, x)

3: 2

step-by-step explanation:

shorter piece is 2: 3, so just reverse it, and you get 3: 2