Question

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)

Answer 1

b. T <7,-2> (RSTU); (2,-1)

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;

`(x,y)\to (x+a,y+b)`

Then the point R(-5,-5) has the image;

`R(-5,-5)\to R'(-5+a,-5+b)=R'(2,-7)`

This implies that;

`-5+a=2`

`\Rightarrowa=2+5=7`

and

`-5+b=-7`

`\Rightarrow b=-7+5`

`\Rightarrow b=-2`

Therefore the translation rule is T(7,-2)

Hence;

`U(-5,1)\to U'(-5+7,1-2)=U'(2,-1)`

the correct choice is B.