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

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;

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

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.