Question

Point 2, 6) on triangle where is new point after rotation of 90 degrees counterclockwise

Answer 1

To determine the new coordinates of point (2, 6) after a 90-degree counterclockwise rotation, we can use the rotation matrix formula:

[x', y'] = [x * cos(theta) - y * sin(theta), x * sin(theta) + y * cos(theta)]

Here, theta represents the angle of rotation (90 degrees in this case), and (x, y) are the original coordinates of the point.

Plugging in the values, we get:

[x', y'] = [2 * cos(90) - 6 * sin(90), 2 * sin(90) + 6 * cos(90)]

Since cos(90) = 0 and sin(90) = 1, the equation simplifies to:

[x', y'] = [0 - 6, 2 + 6] = [-6, 8]

Thus, the new coordinates after a 90-degree counterclockwise rotation would be (-6, 8).