Question

parallelogram efgh is shown in the coordinate plane. efgh is rotated 90° clockwise about the origin and then translate it 3 units down. if the coordinates of a resultant point is (1, - 4), what were the coordinates of the original point? e(1,1) f(2,5) g(4,5) h(3,1)

Explanation:

Step1: Reverse the translation

The translation is 3 units down. To reverse it, we add 3 to the y - coordinate of the resultant point.
Let the resultant point be $(x_1,y_1)=(1, - 4)$. After reversing the translation, the point before translation is $(x_2,y_2)=(1,-4 + 3)=(1,-1)$.

Step2: Reverse the rotation

The rule for a $90^{\circ}$ clock - wise rotation about the origin is $(x,y)\to(y,-x)$. To reverse a $90^{\circ}$ clock - wise rotation (i.e., perform a $90^{\circ}$ counter - clockwise rotation), we use the rule $(x,y)\to(-y,x)$.
For the point $(x_2,y_2)=(1,-1)$, after reversing the rotation, the original point $(x_3,y_3)=(-(-1),1)=(1,1)$.

Answer:

$(1,1)$