Question

e vertices of a rectangle are R(-5,-5), S(-6,-5),T(-1,1),U(-5,1) a translation maps R to the point (2,-9)

Answer 1

Answer:

The rule of translation : $(x,y)\rightarrow (x+7,y-4)$

The vertices of image is R'(2,-9), S'(1,-9), T'(6,-3) and U'(2,-3).

Step-by-step explanation:

The vertices of a rectangle are R(-5,-5), S(-6,-5), T(-1,1), U(-5,1).

It is given that a translation maps R to the point (2,-9).

Difference between x-coordinates:

$-5-2=-7$

Difference between y-coordinates:

$-5-(-9)=-5+9=4$

The x-coordinate increased by 7 and y-coordinate decreased by 4. It means the figure shifts 7 units right and 4 units down.

The rule of translation is

$(x,y)\rightarrow (x+7,y-4)$

The vertices of image are

$R(-5,-5)\rightarrow R'(-5+7,-5-4)=R'(2,-9)$

$S(-6,-5)\rightarrow S'(-6+7,-5-4)=S'(1,-9)$

$T(-1,1)\rightarrow T'(-1+7,1-4)=T'(6,-3)$

$U(-5,1)\rightarrow U'(-5+7,1-4)=U'(2,-3)$

Therefore, the vertices of image are R'(2,-9), S'(1,-9), T'(6,-3) and U'(2,-3).