Respuesta :
The coordinates of the vertices [tex]R(-2,5)[/tex], [tex]S(4,2)[/tex] and [tex]T(-1,-1)[/tex] will be [tex]R'(-5,-2)[/tex], [tex]S'(-2,4)[/tex] and [tex]T'(1,1)[/tex] after rotating [tex]90^{\circ}[/tex]counterclockwise about the origin.
What is the transformation rule for rotation?
Rotation is a transformation in which a point or a figure is rotated clockwise or counterclockwise by an angle (called rotation angle) with respect to a point or a line ( called the center of rotation or the axis of rotation).
After rotating a point [tex]P(x,y)[/tex] counter-clockwise by an angle [tex]\theta[/tex] with respect to the origin, the new coordinates of the point will be: [tex]P'(x',y')[/tex] where, [tex]x'=x\cos\theta-y\sin\theta[/tex] and [tex]y'=x\sin\theta+y\cos\theta[/tex].
Here, the vertices [tex]R(-2,5)[/tex], [tex]S(4,2)[/tex] and [tex]T(-1,-1)[/tex] are rotated [tex]90^{\circ}[/tex]counterclockwise about the origin.
So, the new coordinates of [tex]R(-2,5)[/tex] will be: [tex]R'(-2\cos90^{\circ}-5\sin90^{\circ}, -2\sin90^{\circ}+5\cos90^{\circ})[/tex] i.e., [tex]R'(-5,-2)[/tex].
The new coordinates of [tex]S(4,2)[/tex] will be: [tex]S'(4\cos90^{\circ}-2\sin90^{\circ}, 4\sin90^{\circ}+2\cos90^{\circ})[/tex] i.e., [tex]S'(-2,4)[/tex].
The new coordinates of [tex]T(1,-1)[/tex] will be: [tex]T'(1\times \cos90^{\circ}-(-1)\times\sin90^{\circ}, 1\times \sin90^{\circ}+(-1)\times\cos90^{\circ})[/tex] i.e., [tex]T'(1,1)[/tex].
Therefore, the coordinates of the vertices [tex]R(-2,5)[/tex], [tex]S(4,2)[/tex] and [tex]T(-1,-1)[/tex] will be [tex]R'(-5,-2)[/tex], [tex]S'(-2,4)[/tex] and [tex]T'(1,1)[/tex] after rotating [tex]90^{\circ}[/tex]counterclockwise about the origin.
To know more about rotation, refer: https://brainly.com/question/26249005
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