Question

A triangle with points 1, -1 3, -2 and 1 negative 3 rotated 90 degrees counter clockwise What is the translation

Answer 1

To find the new coordinates of a triangle after a 90-degree counterclockwise rotation around the origin, we can use the rotation transformation. The transformation rule for rotating a point \((x, y)\) 90 degrees counterclockwise is given by the formulas:

\[
(x', y') = (-y, x)
\]

Let's apply this rotation to each of the vertices of the triangle:

1. **Point (1, -1)**:
\[
x' = -(-1) = 1
\]
\[
y' = 1
\]
So, the new coordinates are **(1, 1)**.

2. **Point (3, -2)**:
\[
x' = -(-2) = 2
\]
\[
y' = 3
\]
So, the new coordinates are **(2, 3)**.

3. **Point (1, -3)**:
\[
x' = -(-3) = 3
\]
\[
y' = 1
\]
So, the new coordinates are **(3, 1)**.

Now, combining these results, after rotating the triangle with vertices at \((1, -1)\), \((3, -2)\), and \((1, -3)\) 90 degrees counterclockwise, the new vertices will be:

- \((1, 1)\)
- \((2, 3)\)
- \((3, 1)\)

If you want to translate the triangle (shift it without rotation), you'll need to specify a direction and distance of the translation. The problem as you've stated it is just about the rotation. If there's an additional translation you'd like to apply, please provide those details!