Question

An illustration of a coordinate plane with four quadrants shows the x and y axes extending from negative 8 to 8 in increments of 1. A triangle A B C is plotted on the graph. The triangle A B C has its vertices marked with closed points at A left parenthesis 2 comma 4 right parenthesis, B left parenthesis 6 comma 6 right parenthesis, and C left parenthesis 6 comma 2 right parenthesis.

Given point A (2, 4) on the triangle in Quadrant I, where is the new point if the triangle is rotated 90 degrees counterclockwise?

Answer 1

To find the new position of point A (2, 4) after rotating the triangle 90 degrees counterclockwise around the origin, we can use the following transformation:

When rotating a point \((x, y)\) 90 degrees counterclockwise, the new coordinates \((x', y')\) are given by:
\[
(x', y') = (-y, x)
\]

Now, applying this transformation to point A (2, 4):
- The x-coordinate becomes \(-4\)
- The y-coordinate becomes \(2\)

Thus, the new coordinates of point A after the rotation are:
\[
A' = (-4, 2)
\]

So point A (2, 4) after a 90-degree counterclockwise rotation will be located at \((-4, 2)\).