Question

Rotate ABC 90° counterclockwise using pointP as the center of rotation.A':___ B':___ C':___

Answer 1

To rotate ΔABC 90º counterclockwise using the point P as the center of rotation, the first step is to subtract the coordinates of P to the coordinates of each vertex of the triangle:

1) Subtract P(-2,1) to each vertex:

A(0,-2) → A(0-(-2),-2-1) → A(2,-3)

B(-2,-3) → B((-2)-(-2),(-3)-1) → B(0,-4)

C(-1,-5) → C((-1)-(-2),(-5)-1) → C(1,-6)

2) Following the rule, perform the rotation 90º counterclockwise about the origin:

`(x,y)\to R_(90CW)\to(-y,x)`

A(2,-3) → A(-(-3),2) → A(3,2)

B(0,-4) → B(-(-4),0) → B(4,0)

C(1,-6) → C(-(-6),1) → C(6,1)

3) Add P(-2,1) to each vertex:

A(3,2) → A'(3+(-2),2+1) → A'(1,3)

B(4,0) → B'(4+(-2),0+1) → B'(2,1)

C(6,1) → C'(6+(-2), 1+1) → C'(4,2)

So, the coordinates of ΔA'B'C' are:

`\begin{gathered} A^(\prime)(1,3) \\ B^(\prime)(2,1) \\ C(4,2) \end{gathered}`