The vertices of a rectangle are r(-5,-5), S(-1,-5), T(-1,1), and U(-5,1). A translation maps R to the point (-4,2). find the translation rule and image of U

Question

anonymous · Answer

$$
\ \ f(x,y)=(x+\Delta{x},y+\Delta{y})\
\ \ f(-5,-5)=(-4,2)\
\ \ (-5+\Delta{x},-5+\Delta{y})=(-4,2)\
\text{So now we can determine }\Delta{x},\Delta{y}.\
\ \ -5+\Delta{x}=-4\
\ \ \Delta{x}=1\
\ \ -5+\Delta{y}=2\
\ \ \Delta{y}=7\
\text{So we know our translation rule is...}\
\ \ f(x,y)=(x+1,y+7)\
\text{Thus we can determine the image of U as follows.}\
\ \ f(-5,1)=(-5+1,1+7)=(-4,8)
$$