Question

In a video game an object represented by the point (2,7) is rotated counterclockwise 175 degrees around an origin. What are the new coordinates that represent the point?

Answer 1

(-2.60, -6.80)

Explanation:

The new coordinates can be found by multiplying by the rotation matrix:

`\left[\begin{array}{c}x'&y'\end{array}\right]=\left[\begin{array}{cc}cos(\theta)&-sin(\theta)\\sin(\theta)&cos(\theta)\end{array}\right]\left[\begin{array}{c}x&y\end{array}\right]`

That is, ...

x' = x·cos(175°) -y·sin(175°) = 2(-0.9962) -7(0.0872) = -2.60

y' = x·sin(175°) +y·cos(175°) = 2(0.0872) +7(-0.9962) = -6.80

The new coordinates are ...

(x', y') = (-2.60, -6.80)