Question

given point A(2,6) on the triangle, where would the new point on the triangle be after rotating 90 degrees clockwise?

Answer 1

wrong

Answer 2

To rotate a point 90 degrees clockwise, we need to swap the x and y coordinates and change the sign of the new y coordinate.

Given the point A(2, 6), after rotating 90 degrees clockwise, the new point would be (-6, 2).

Please note that this rotation is performed with respect to the origin (0,0) as the center of rotation.

Answer 3

Apologies for the mistake.
To rotate a point 90 degrees clockwise, we need to use the following rotation matrix:

|cosθ -sinθ|
|sinθ cosθ|

Since we want to rotate the point A(2,6) 90 degrees clockwise, θ would equal -90 degrees or -π/2 radians.

Using the rotation matrix, we can find the new coordinates by multiplying the matrix by the vector representing the coordinates of point A:

|cos(-π/2) -sin(-π/2)| |2| |x'|
|sin(-π/2) cos(-π/2)| * |6| = |y'|

Simplifying this equation:

|0 1| |2| |x'|
|-1 0| * |6| = |y'|

Which results in:

0 * 2 + 1 * 6 = x' => 6 = x'
-1 * 2 + 0 * 6 = y' => -2 = y'

So, after rotating 90 degrees clockwise, the new point on the triangle would be (-2, 6).