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 (2,-7). find the translation rule and the image of U. a. T <-7,-2> (RSTU); (-12,-1) b. T <7,-2> (RSTU); (2,-1) c. T <7,2> (RSTU); (2,3) d. T <-7,2> (RSTU); (-12,3)

Accepted Solution

Answer:b. T <7,-2> (RSTU); (2,-1) Step-by-step explanation:The given triangle has vertices R(-5, -5), S(-1,-5), T(-1,1) and U(-5,1).Let the translation rule be T(a,b).Then the mapping for the translation will be;[tex](x,y)\to (x+a,y+b)[/tex]Then the point R(-5,-5) has the image;[tex]R(-5,-5)\to R'(-5+a,-5+b)=R'(2,-7)[/tex]This implies that;[tex]-5+a=2[/tex] [tex]\Rightarrowa=2+5=7[/tex] and[tex]-5+b=-7[/tex] [tex]\Rightarrow b=-7+5[/tex] [tex]\Rightarrow b=-2[/tex] Therefore the translation rule is T(7,-2)Hence;[tex]U(-5,1)\to U'(-5+7,1-2)=U'(2,-1)[/tex]the correct choice is B.