90 and 270 degree rotations Quick check

Question

What is the point when you rotate a geometric figure with point (5,8) 207° counterclockwise about the origin (a) (-8,-5)

Answer 1

To find the point after a 207° counterclockwise rotation about the origin, you can use the rotation matrix:

[ cos(θ) -sin(θ) ]
[ sin(θ) cos(θ) ]

In this case, θ = 207°.

Plugging the values into the matrix, we get:

[ cos(207°) -sin(207°) ]
[ sin(207°) cos(207°) ]

Evaluating the trigonometric functions, we have:

[ -0.9781 -0.2079 ]
[ -0.2079 -0.9781 ]

To rotate the point (5,8) by this matrix, we multiply as follows:

[ -0.9781 -0.2079 ] x [ 5 ]
[ -0.2079 -0.9781 ] [ 8 ]

= [ (-0.9781)(5) + (-0.2079)(8) ]
[ (-0.2079)(5) + (-0.9781)(8) ]

= [ -4.8905 + (-1.6632) ]
[ -1.0395 + (-7.8254) ]

= [ -6.5537 ]
[ -8.8649 ]

So, the point after rotating (5,8) 207° counterclockwise about the origin is (-6.5537, -8.8649).

However, the point you provided, (-8,-5), is not the correct answer.