What is the new point and you rotated geometric figure with 5, 8 270° counterclockwise about the origin
To rotate a point counterclockwise around the origin, you need to apply the following transformation matrix:
[ cos(theta) -sin(theta) ] [x]
[ sin(theta) cos(theta) ] [y]
In this case, the point is (5, 8) and the angle of rotation is 270° counterclockwise. Converting 270° to radians gives us 3π/2.
Applying the transformation matrix:
[ cos(3π/2) -sin(3π/2) ] [5]
[ sin(3π/2) cos(3π/2) ] [8]
Calculating the trigonometric functions:
[ 0 -1 ] [5]
[ 1 0 ] [8]
Multiplying the matrices:
[ 0 * 5 + (-1) * 8 ]
[ 1 * 5 + 0 * 8 ]
Simplifying:
[ -8 ]
[ 5 ]
Therefore, the new point after rotating (5, 8) 270° counterclockwise about the origin is (-8, 5).