∆ABC is plotted on a coordinate plane. If ∆ABC rotates 90° clockwise around point C, what are the coordinates of A'?
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Say, (a1,a2) and (c1,c2) be the co-ordinates of the points A and C respectively. Say the origin is denoted by O.
The vectors OA and OC are given by a1 + ia2 and c1 + ic2 resp.
The vector CA is given by (a1-c1)+ i(a2-c2)
This segment rotates clockwise by 90 degrees around C. This operation is the same as
multiplication by -i. So, the rotated vector is (a2-c2) - i(a1-c1) , call this CA' , A' is the new position of A.
Therefore the vector OA' is given by (a2-c2) - i(a1-c1) + c1 + ic2 = (a2-c2+c1) + i(c2 + c1 - a2) [what we did was simply OA' = CA' + OC, vector addition]
So, the new position of A, that is A' has the co-ordinates ((a2-c2+c1),(c2+c1-a2))
Plug in the values given in your specific problem.