What is the new point and you rotated geometric figure with 5, 8 270° counterclockwise about the origin

Answer 1

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).