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

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

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
`((a)/(2),(b)/(2))`.

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