Geometry: Symmetry transformations
Chained reflections
In a [[$xy$]]-coordinate system, draw a triangle whose vertices are [[$A(3,2)$]], [[$B(1,1)$]], and [[$C(1,4)$]].
Next, make a reflection of triangle [[$ABC$]] with respect to the [[$x$]]-axis (i.e. so that the triangle is reflected upside down). Name the congruent triangle [[$DEF$]].
Next, make a reflection of triangle [[$DEF$]] with respect to the origin [[$O(0,0)$]] (i.e. so that the triangle is reflected to the top left of the coordinate system). Name the congruent triangle [[$GHI$]].
Specify the coordinates of [[$G$]].
Next, make a reflection of triangle [[$ABC$]] with respect to the [[$x$]]-axis (i.e. so that the triangle is reflected upside down). Name the congruent triangle [[$DEF$]].
Next, make a reflection of triangle [[$DEF$]] with respect to the origin [[$O(0,0)$]] (i.e. so that the triangle is reflected to the top left of the coordinate system). Name the congruent triangle [[$GHI$]].
Specify the coordinates of [[$G$]].