Given:
The coordinates of the endpoints of segment BC are B(5,1) and (-3,-2).
Under the transformation [tex]R_{90^\circ}[/tex] the image of [tex]\overline{BC}[/tex] is [tex]\overline{B'C'}[/tex].
To find:
The coordinates of points B' and C'.
Solution:
We know that transformation [tex]R_{90^\circ}[/tex] means 90 degrees counterclockwise rotation about the origin.
If a figure is rotated 90 degrees counterclockwise rotation about the origin, then
[tex](x,y)\to (-y,x)[/tex]
Using this rule, we get
[tex]B(5,1)\to B'(-1,5)[/tex]
Similarly,
[tex]C(-3,-2)\to C'(-(-2),-3)[/tex]
[tex]C(-3,-2)\to C'(2,-3)[/tex]
Therefore, the coordinates of required points are B'(-1,5) and C'(2,-3).
