Given:
The image of point A under a 90° rotation about the origin is A'(10, -4).
To find:
The coordinates of point A.
Solution:
90° rotation about the origin means the figure is rotated 90° counterclockwise about the origin and the rule of rotation is
[tex](x,y)\to (-y,x)[/tex]
Let the coordinates of A are (a,b).
[tex]A(a,b)\to A'(-b,a)[/tex]
The image of point A under a 90° rotation about the origin is A'(10, -4).
[tex]A'(-b,a)=A'(10,-4)[/tex]
On comparing both sides, we get
[tex]-b=10\Rightarrow b=-10[/tex]
[tex]a=-4[/tex]
Therefore, the coordinates of point A are (-4,-10).
