Question

RSTU is a rectangle with vertices at R(-3,1), S(1 ,1), T(-3,3) and U (1, 3). Describe two lines of reflection that would carry the rectangle onto itself. (enter as x = and y =)

Answer 1

Answer:

The two lines of reflection are $x=-1$ and $y=2$

Step-by-step explanation:

I will attach a file with the graph of the rectangle and the lines of reflection.

We know that RSTU is a rectangle with vertices at $R=(-3,1)$ , $S=(1,1)$,

$T=(-3,3)$ and $U=(1,3)$

The first step is to draw the vertices on the plane and them the rectangle.

The rectangle is a symmetrical figure. Therefore if we want to carry the rectangle onto itself using a line of reflection this line must goes through the centroid of the rectangle.

Given that we have a rectangle whose width is $a$ and its length is $b$ its centroid will be place at $(\frac{a}{2},\frac{b}{2})$.

Looking at the graph and using this information we find that the two lines of reflection are $x=-1$ and $y=2$.