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

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).

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).