Question

the image of point A under a 90° rotation about the origin is A'(10, -4). What are the coordinates of point A?

Answer 1

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

`(x,y)\to (-y,x)`

Let the coordinates of A are (a,b).

`A(a,b)\to A'(-b,a)`

The image of point A under a 90° rotation about the origin is A'(10, -4).

`A'(-b,a)=A'(10,-4)`

On comparing both sides, we get

`-b=10\Rightarrow b=-10`

`a=-4`

Therefore, the coordinates of point A are (-4,-10).